Roughness Based Crossflow Transition Control for a Swept Wing Airfoil Design

A high fidelity transition prediction methodology has been applied to a swept airfoil design at a Mach number of 0.75 and chord Reynolds number of approximately 17 million, with the dual goal of an assessment of the design for the implementation and testing of roughness based crossflow transition control and continued maturation of such methodology in the context of realistic aerodynamic configurations. Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes in order to weaken the growth of naturally occurring, linearly more unstable instability modes via a nonlinear modification of the mean boundary layer profiles. Therefore, a synthesis of receptivity, linear and nonlinear growth of crossflow disturbances, and high-frequency secondary instabilities becomes desirable to model this form of control. Because experimental data is currently unavailable for passive crossflow transition control for such high Reynolds number configurations, a holistic computational approach is used to assess the feasibility of roughness based control methodology. Potential challenges inherent to this control application as well as associated difficulties in modeling this form of control in a computational setting are highlighted. At high Reynolds numbers, a broad spectrum of stationary crossflow disturbances amplify and, while it may be possible to control a specific target mode using Discrete Roughness Elements (DREs), nonlinear interaction between the control and target modes may yield strong amplification of the difference mode that could have an adverse impact on the transition delay using spanwise periodic roughness elements. Nomenclature Ainit = initial amplitude of crossflow instability mode or secondary instability mode C, c = wing chord length measured in direction perpendicular to leading edge f = frequency of instability oscillations M = freestream Mach number N = N-factor of linear crossflow instability or secondary instability Rec = Reynolds number based on wing chord X, x = chordwise coordinate in direction perpendicular to leading edge Y = wall-normal coordinate Z = spanwise coordinate in direction parallel to leading edge Λ = wing sweep angle λ = spanwise wavelength of crossflow instability in millimeters in direction parallel to leading edge I. Background ubstantial reductions in the fuel burn of future aircraft have been targeted both in the U.S. and in Europe in order to lower the cost of air travel and alleviate the impact of aviation on the environment. A substantial fraction of the targeted reductions in aircraft fuel burn will come from the reductions in vehicle drag. For today’s commercial transport aircraft, up to one half of the total drag corresponds to skin friction drag. Because laminar skin friction is much lower in comparison with the turbulent skin friction, flow control via delayed boundary-layer transition over major aerodynamic surfaces holds the potential to provide the desired reductions in the overall drag. S 28th AIAA Applied Aerodynamics Conference 28 June 1 July 2010, Chicago, Illinois AIAA 2010-4380 This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. American Institute of Aeronautics and Astronautics 2 NASA’s Subsonic Fixed Wing Project is investigating several options to help develop robust technology concepts for laminar flow control and to accelerate their insertion into the operational fleet. One of those concepts involves the delay of crossflow-induced transition over a swept aerodynamic surface using control input in the form of appropriately positioned Discrete Roughness Elements (DREs) near the leading edge. A bulk of the existing experimental and computational studies of the DRE concept have been carried out for either incompressible or supersonic configurations with modest wing-chord Reynolds numbers of up to approximately 8 million, and with pressure distributions that may not be optimal for wing designs for subsonic transport aircraft flying at Mach numbers between 0.75 to 0.90. Consequently, additional effort is deemed necessary to assess the potential capability of the DRE concept to control swept wing transition at transonic Mach numbers and substantially higher chord Reynolds numbers than previous applications. Given the sensitivity of transition to wind tunnel disturbances and the cost of flight experiments, computational tools will need to play an important role in the assessment of DREs for subsonic transport vehicles, as a means of risk reduction as well as to help optimize the DRE design. The DRE concept seeks to delay transition via controlled seeding of subdominant crossflow modes that cannot lead to transition on their own, but can keep the naturally dominant instability modes at bay via nonlinear modification of the basic state and/or mode competition. This intrinsically nonlinear control mechanism calls for a higher fidelity prediction approach involving all of the relevant stages of the transition process, namely, receptivity, linear and nonlinear growth of primary crossflow instabilities, and secondary instability. The individual ingredients of this approach have been available for some time and partial integration of those ingredients has been demonstrated in prior works. Computations along this line have been performed for the low Mach number configuration of the flight experiment at chord Reynolds numbers of 7 to 8 million. The results show that the most unstable stationary crossflow mode is weakened in the presence of roughness elements, with an accompanying reduction in the growth potential of the high-frequency secondary instability modes that are likely to cause the onset of laminar-turbulent transition. However, the same results also indicate that the control mode amplitudes required to stabilize the dominant modes can become excessively large, especially when the maximum N-factors are rather large, so that the possibility of premature transition due to overcontrol cannot be entirely discounted. Similar findings have also been obtained for a supersonic swept wing configuration at Mach 2.4 and chord Reynolds number of 16 million. In recent work, Texas A & M University has performed a conceptual design study of a Laminar Flow Control (LFC) flight test with target conditions of M ≈ 0.75, a chord Reynolds number, Rec, between 15 and 20 million, and a leading-edge sweep angle, Λ, of 30°. The resulting wing has significant potential for natural laminar flow over both suction and pressure surfaces at the design angle-of-attack of 0 degrees. At off-design conditions, however, an earlier transition may occur as a result of stationary crossflow modes, which opens up the possibility of roughness based transition control on the same model, either to increase the lift coefficient or to extend the angle-of-attack range for laminar flow. The broad objectives behind the present effort are to assess the feasibility of achieving DRE based transition control using NASA’s prediction tools for receptivity, nonlinear development and secondary instability stages of the transition process and, in doing so, to help mature those prediction tools and the methodology to apply them in a practical context. II. Flow Configuration and Analysis Codes The design process for the laminar flow airfoil TAMU-003T-75(v.90) has been described in ref. 13 and also reported in a companion paper. In brief, the 9.3 percent thick, 30-degree swept airfoil is designed to achieve natural laminar flow over 60 and 50 percent of the suction and pressure surfaces, respectively, at the design condition of zero degree angle of attack, Mach number of M = 0.75, and chord Reynolds number of approximately 17 million based on free-stream speed, a streamwise chord length of 12 ft, and free-stream temperature of 390 R, corresponding to a flight altitude of 40,000 ft. Design constraints for the wing included (i) a lift coefficient that is typical of subsonic transports, and (ii) a wing thickness distribution that is suitable for a mid-size business jet. Both Tollmien-Schlichting and crossflow instabilities are sufficiently weak at the design angle of attack, so that natural laminar flow should be achievable over a significant portion of the airfoil surface (x/c>0.6 on suction surface and x/c>0.5 on the pressure side) without any external means of boundary layer control. In this paper, we focus on the off design condition corresponding to an angle of incidence equal to -1 degree. At this condition, a stronger crossflow instability exists along the suction side and, hence, could provide a potential means to assess DRE based laminar flow technology at higher Reynolds numbers than previous tests.