A Transonic Laminar-Flow Wing Glove Flight Experiment: Computational Evaluation and Linear Stability

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1 30th AIAA Applied Aerodynamics Conference June 2012, New Orleans, Louisiana AIAA A Transonic Laminar-Flow Wing Glove Flight Experiment: Computational Evaluation and Linear Stability Matthew W. Roberts 1, Helen L. Reed 2, William S. Saric 3, Texas A&M University, College Station, TX A The Flight Research Laboratory at Texas A&M University has proposed conducting both natural laminar flow and passive laminar flow control flight test experiments through NASA s Environmentally Responsible Aviation program in partnership with the Dryden Flight Research Center and the Langley Research Center. The flight test program will further explore discrete roughness element technology and demonstrate its effectiveness at extending laminar flow beyond the natural transition location. Texas A&M has completed a wing glove design, designated TAMU-06-05, that will be installed on a Gulfstream III testbed aircraft. Detailed analysis on the wing glove design effectiveness is given, focusing on flowfield behavior and boundary-layer stability characteristics near the glove using fullaircraft CFD calculations. AoA = angle of attack C l = sectional lift coefficient C L = area lift coefficient C p = pressure coefficient M = Mach number N = Smith Van-Ingen N-factor Re c = chord Reynolds number x/c = chord length ratio Nomenclature I. Introduction VIATION fuel prices have experienced a significant increase in the past decade and as such, commercial airlines have seen a rise in operating expenses. The response to the fuel cost problem has been a push to improve aircraft fuel efficiency. Several possibilities exist to accomplish this goal, such as advances in engine technology, decreases in aircraft weight through the use of composite materials, and increases in laminar flow over the aircraft. Laminar flow in particular is promising because laminar skin friction can be up to 90% less than its turbulent counterpart 1 and skin friction represents roughly half of the total drag budget for transport aircraft 2. While laminarizing an entire aircraft is unlikely, substantial gains can be made on the wings and empennage which could reduce the total drag by as much as 10%. Obtaining laminar flow, however, is a challenging proposition. For swept-wing configurations characteristic of transport aircraft, the crossflow instability represents the largest hurdle to overcome in the attempt to increase amounts of laminar flow 3,4. One of the simplest methods employed to curb crossflow instability growth is to use unswept wings. However, this is typically deemed infeasible for transonic aircraft because of the wave drag penalties associated with such a design. Another option is to use a highly-polished leading edge. It has been shown that the transition location is rather sensitive to surface roughness, especially near the leading edge 5. Unfortunately, keeping an operational wing surface polished to required levels could prove to be difficult. The use of an active suction system is another possibility and has actually been successfully demonstrated in a number of test flights over the years 1. Anticipated manufacturing and operational concerns have been the biggest detractors in implementing such a system. If none of these options are desirable, one final possibility to control crossflow is to use a passive array of discrete roughness elements (DREs) to create nonlinear biasing of stationary crossflow wave growth near the attachment line. This suppresses the growth of unstable crossflow waves that would otherwise cause transition 6,7. 1 Graduate Student, Department of Aerospace Engineering, Member AIAA 2 Professor, Department of Aerospace Engineering, Fellow, AIAA 3 Distinguished Professor, Department of Aerospace Engineering, Fellow, AIAA 1 Copyright 2012 by the, Inc. All rights reserved.

2 DRE technology has already been demonstrated in the wind tunnel 6 and in flight 8,3 up to chord Reynolds numbers of The next major step is to show DRE effectiveness at increased Reynolds numbers. The Flight Research Laboratory (FRL) at Texas A&M University has proposed conducting a flight test experiment investigating natural laminar flow (NLF) and laminar flow control using DREs, which will henceforth be referred to as the swept wing laminar flow control (SWLFC) technique, at chord Reynolds numbers between and The experiment is funded by NASA s Environmentally Responsible Aviation program and supported by NASA Langley Research Center (LaRC) and NASA Dryden Flight Research Center (DFRC). A wing glove outfitted to a business-class jet represented the ideal configuration to perform such as experiment. The aircraft selected to serve as the experimental testbed is a Gulfstream III owned and operated by NASA DFRC. Figure 1 shows a planform view of the glove installed on the port wing of the aircraft with reference dimensions included. A more detailed overview of the flight test configuration is given in the companion paper Belisle et al (9), including planform design and the optimization work responsible for generating the glove outer mold line (OML). In the configuration numbering system implemented by FRL, this OML has been designated TAMU Figure 1. Planform layout of the TAMU wing glove. Table 1. Target flight conditions for the wing-glove flight test experiment. Parameter Value Mach Number Altitude Range 9,140-13,720 m (30,000-45,000 ft) NLF Re c Range SWLFC Re c Range The target flight conditions for the experiment are given above in Table 1. A feasibility study showed that an experiment of this nature was within the realm of possibility 10. Analysis performed on an earlier wing glove design, given by Belisle et al (11) and designated TAMU-05-04, showed improvements could be made. An updated design has since been completed 12 and is the focus of this paper and its companion paper 9. This paper, in particular, addresses the computational evaluation of the wing glove design in its installed configuration on the testbed aircraft. Two principal areas will be investigated: 1) the aerodynamic effects of the flowfield created by both the aircraft and wing glove and 2) the boundary-layer stability characteristics of the wing glove under the influence of a full-aircraft flowfield. The central goal is to determine the effectiveness of the current glove design for the demonstration of DRE technology at operationally relevant Reynolds numbers. 2

3 II. CAD Model Development The first step in the CFD process is to develop a CAD model that is both representative of the real geometry and conducive to the grid generation process. A laser scan of the G-III testbed that had been completed previously provided the initial CAD model from which to work from 11. The SolidWorks CAD package, developed by Dassault Systemes, was used to perform all CAD-related tasks. Several simplifications from the baseline model were made to facilitate the overall CFD process. Past experience on similar projects showed that the empennage had a negligible effect on the flowfield near the wing 10,13,14, leading to its exclusion from all G-III models. Certain areas of the scanned model also contained a significant level of geometric complexity. Fine details that would have no influence on the flowfield near the glove should be eliminated to avoid an unnecessarily exorbitant cell count. The engine nacelle, which included thrust reverser and hush kit geometry, was one such area in need of simplification. These features were removed and replaced with surfaces that blend smoothly into the existing engine nacelle surface while keeping the outlet location and area unchanged. This modification is illustrated in Figure 2. Finally, a symmetric configuration was assumed, requiring the modeling of only one half of the aircraft. Even though the port and starboard sides would differ due to the presence of the glove, it would be much less expensive computationally to only model the port half of the aircraft. It should be noted, however, that if the flow was asymmetric, i.e. nonzero sideslip, a model of the entire aircraft would be necessary. Figure 2. Comparison of engine geometric detail: a) scanned model, b) simplified model. Supplemental geometry was also created to assist with the grid generation process. This included defining boundaries of the different mesh zones, which are discussed in the following section, as well as further processing the existing aircraft surface geometry, such as adding split lines, to make surface mesh creation more conducive. These tasks were completed prior to grid generation because the SolidWorks CAD package is better suited for this sort of work than the meshing software described below. III. Computational Grid Generation A. Grid Setup The meshing software ICEM CFD 13.0 was used to generate the computational grids for this project. It is developed, along with the CFD solver FLUENT, by ANSYS, Inc. A hybrid grid format that included both structured and unstructured cells was used. The grid was divided into three nested zones: the freestream zone, the aircraft zone, and the glove zone. The glove zone was further divided into the laminar subzone and the turbulent subzone. Working inward, the freestream zone is the first level of the nested grid structure. It defines the extent of the computational domain and is the largest zone by volume. The freestream zone was blocked and meshed with structured hexahedral cells. Correctly sizing the farfield is an important step for the entire CFD process. Following the grid generation guidelines outlined by the Fourth AIAA CFD Drag Prediction Workshop 15 (DPW), all farfield boundaries were placed at least 100 reference chord-lengths away from all aircraft surfaces. The sizing of the 3

4 farfield was investigated in the grid independence studies described in the following section. Figure 3 displays the freestream zone mesh with the aircraft zone boundary labeled for perspective. Figure 3. Freestream zone mesh. The aircraft zone is the second level of the nested grid structure and contains a majority of the aircraft geometry. Due to the complex shape of the aircraft, this zone was meshed with unstructured tetrahedral, pyramidal, and prismatic cells. Much of the aircraft zone is composed of tetrahedral cells, though pyramidal and prismatic cells were implemented in select locations. The use of pyramidal cells to transition from hexahedral cells to tetrahedral cells eliminates the need for zonal interfaces between the freestream and aircraft zones. Prismatic cells assist in resolving the flowfield near the aircraft surface where viscous effects are significant. The DPW 15 was again referenced when creating the aircraft surface mesh. Figure 4 shows the aircraft zone mesh and includes the glove zone boundary for reference. Figure 4. Aircraft zone mesh. The glove zone is the third and final major level of the nested grid structure. It contains a large portion of the wing, including the wing glove. Structured hexahedral cells were the optimal choice for this zone for several 4

5 reasons. First and foremost, unstructured cells would most likely not provide sufficient wall-normal mesh resolution for boundary-layer stability calculations. Second, structured cells offered considerably more control over the mesh design than unstructured surface and prismatic cells. Finally, unstructured cells were not conducive to the flowfield data extraction techniques employed to complete boundary-layer stability calculations. Establishing the location and extent of the zone boundary was not a trivial matter. Because a mesh interface was required to pass flowfield information from the aircraft zone to the glove zone, there was a concern that placing the interfaces too close to the area of interest could skew the results there. This aspect of the grid was also investigated during the grid independence studies. Figure 5 displays the glove zone mesh. Figure 5. Glove zone mesh. Early CFD simulations indicated that using a laminar flow model would cause solution convergence issues, with the likely culprit being flow separation. This is not entirely surprising because similar difficulties were encountered in past projects 13,14. Using a turbulence model assists with this problem; however, a turbulent boundary layer cannot be used for boundary-layer stability calculations. The solution was to split the glove zone into two subzones: a laminar subzone, where the flow would employ a laminar model, and a turbulent subzone, where a turbulence model would be used. The laminar subzone mesh, shown below in Figure 6, must be created in a careful and specific manner because it will contain the flowfield information used in all boundary-layer stability calculations. The boundary layer above the wing glove test section is the primary concern so the spanwise boundaries of the laminar subzone were set to coincide with those of the test section. The outer boundary of the laminar subzone was offset 50.8 mm (2 in) from the wing and glove surfaces, well outside the test section boundary layer region. The location of the aft boundary of the laminar subzone was the most difficult to determine. Flow separation was occurring with a laminar flow model somewhere near the portion of the test section that began to blend back into suction-side wing OML. It was discovered that this could be avoided by ending the laminar subzone slightly before the suction-side pressure minimum and switching back to a turbulent model aft of this location. Through an iterative process, the aft boundary of the laminar subzone was placed at 60% x/c on both sides of the test section. Figure 6. Laminar subzone mesh. The mesh within the laminar subzone must not only capture the flowfield at a proper resolution, but satisfy the needs of boundary-layer data extraction performed after the CFD simulation. Surface mesh construction plays a 5

6 large role in both these goals. Boundary-layer stability is sensitive to changes in the flowfield near the leading edge, making it important to place a large number of cells in this region to accurately resolve large gradients. Spanwise grid lines are tightly packed near the leading edge initially, but are allowed to expand downstream. They are also specifically arranged to lie at constant x/c locations across the glove span to facilitate the flowfield data extraction process. The streamwise grid lines are placed at constant span locations for similar extraction reasons. Moving away from the glove surface, it is critical to obtain a fine wall-normal mesh resolution because boundary-stability calculations require a well-resolved boundary-layer profile. The baseline mesh configuration in the laminar subzone used an initial cell layer height of 2.54 μm ( in) and a wall-normal geometric growth rate of This corresponds to 60 wall-normal points in the first 1.27 mm (0.05 in) and 122 total points in the laminar subzone. B. Grid Independence Studies Assessing the credibility of CFD modeling and simulation is a vital step for any computational effort. The two primary methods used to accomplish this are verification and validation. The AIAA Guide for Verification and Validation 16 (V&V) describes verification as providing evidence that the model is solved correctly, even though it may not represent the real world solution. Validation, on the other hand, evaluates whether the CFD model, meaning the mathematical and computer code representation of the physical system, is solved accurately with regard to experimental data and observations. Because this project is still in the design stage and no experimental data exists yet, validation will not be addressed in this paper. Verification of the CFD model, however, can be performed. To determine how varying grid parameters affect the solution, CFD simulations were performed using different grids. The results obtained from these simulations could then be compared to results from a CFD simulation using a baseline grid. The flowfield solution in the laminar subzone serves as the area-of-interest for these grid independence studies. Glove C p and boundary-layer stability results were used as the principal criteria to judge independence. Three comparison grids were generated for this analysis: a farfield grid, an interface grid, and a refined grid. Except for the geometry or parameter changes under investigation, they are all nearly identical to the baseline grid. The farfield grid explores how modifying the extent of the computational domain affects the region of interest. For this study, the farfield boundary was reduced by roughly 45% in all three directions. The interface grid examines how moving the location of the aircraft/glove zone interface by altering the size of the glove zone changes the solution near the glove test section. The boundary normal and spanwise offset distances from the test section were reduced by 38%. Finally, the refined grid involved refining the aircraft and glove zones. Most of the refinement effort was focused on the laminar subzone, especially the wall-normal resolution, to ensure the boundary-layer stability behavior did not change. Table 2 gives the specific changes for these three grids (highlighted in gray) along with the baseline grid for comparison. 6

7 Cell Count Laminar Subzone Refinement Interface Offset Domain Size Table 2. Grid geometry and parameters. Baseline Grid Farfield Grid Interface Grid Refined Grid Spanwise m (1,500 ft) m (833.3 ft) m (1,500 ft) m (1,500 ft) Vertical m (3,000 ft) m (1,667 ft) m (3,000 ft) m (3,000 ft) Streamwise 1,372 m (4,500 ft) m (2,708 ft) 1,372 m (4,500 ft) 1,372 m (4,500 ft) Normal m (60 in) m (60 in) m (37.5 in) m (60 in) Spanwise m (98 in) m (98 in) m (60 in) m (98 in) First Layer Height 2.54 μm ( in) 2.54 μm ( in) 2.54 μm ( in) 1.27 μm ( in) Growth Rate Points on Airfoil Freestream Zone Aircraft Zone Glove Zone Total The section C p plots chosen for comparison of these studies are taken from BL204, BL234, and BL264, where BL stands for buttock line. The buttock line number gives the span location in inches away from the center symmetry plane of the aircraft. This notation will be used throughout this paper to reference span locations on the glove. For reference, BL198 marks the inboard extent of the test section and BL270 marks the outboard extent of the test section (see Figure 1). Boundary-layer stability results for stationary crossflow using linear stability theory (LST) were generated for the suction side of the airfoil section at BL234, which is at the midspan location of the glove. Due to the sensitivity of the boundary-layer stability to small changes in the flowfield, the stability results will serve as the true litmus test whether grid independence has been achieved. For the purpose of showing grid independence, the focus should remain how the solution varies from grid to grid and not the behavior of the solution itself. Figure 7 displays the C p results and Figure 8 gives the boundary-layer stability results in the form of an N- factor plot. The agreement between the results from all grids was quite good. There were essentially no differences in the test section C p plots back to 60% x/c or the stability characteristics at BL234. This verified that the baseline grid sufficiently captures the flowfield effects desired for this project and was therefore used in all CFD calculations. 7

8 Figure 7. Comparison of grid-independence study C p results at a) BL204, b) BL234, and c) BL264. Figure 8. Comparison of grid-independence study LST crossflow N-factor results at BL234. 8

9 IV. Full-Aircraft CFD Calculations The CFD simulations conducted for the wing glove design analysis were performed with the full-aircraft configuration in order to account for flowfield effects caused by the presence of the fuselage and the engine near the wing glove. These simulations will not only provide flowfield results, but serve as the source of the mean flow data used in boundary-layer stability calculations. The commercial CFD package FLUENT 13.0 was used for all project simulations. A local workstation was used for many pre- and post-processing activities while the solution calculations were completed through batch processing on the remote supercomputer cluster Eos operated by the Texas A&M Supercomputing Facility. Simulations performed on Eos made use of 32 processors acting in parallel over 8 nodes with 176 GB of memory available. Some simulation pre-processing, such as case setup, was also carried out on Eos. A. Solver Options and Solution Strategies FLUENT gives the user the option of using either a pressure-based or density-based solver. The density-based solver was chosen because compressibility effects are appreciable in the transonic regime. The ideal gas law and Sutherland s law were used for air density and viscosity modeling respectively. All simulations were assumed to be steady state. As alluded to earlier, the use of a turbulence model was necessary because a laminar model caused solution convergence difficulties because of flow separation. The two-equation k-ω shear-stress-transport (SST) turbulence model developed by Mentor 17 was selected because it blends the robust and accurate formulation of the k-ω model near the wall with the freestream independence of the k-ε model in the farfield. However, a laminar model would still be required near the glove surface in order to perform meaningful boundary-layer stability calculations. FLUENT fortunately allows the user to turn off turbulence modeling in a particular region, such as the laminar subzone described earlier, effectively making it laminar. This is accomplished by disabling turbulence production and turbulent viscosity within the cell zone while still transporting the turbulence quantities. Boundary conditions were applied to the farfield, engine inlet, and engine outlet. The farfield boundary used a pressure farfield with conditions drawn from the desired simulation test point parameters. Test points define the flight conditions that generate the near-aircraft flowfield under investigation. For this project, test points consist of a freestream Mach number, aircraft AoA, and chord Reynolds number at a given span location, e.g. BL234. The Mach and Reynolds numbers allow for the calculation of the freestream pressure and temperature, as well as the altitude, using the 1976 U.S. Standard Atmosphere model. Calculating the altitude ensures the test point is within the aircraft flight envelope and can also be used as a substitute for the Reynolds number to define a test point if desired. The engine inlet and engine outlet were modeled with a pressure outlet and pressure inlet respectively. NASA DFRC provided the boundary conditions for the engine modeling, using a 1-D code to obtain pressure, temperatures, and mass flow rates. An implicit formulation, Roe-FDS flux type, and Green-Gauss node-based spatial discretization scheme were selected. Simulations were completed with second-order upwind schemes for flow, turbulent kinetic energy, and specific dissipation rate spatial discretization. Scaled residuals of the governing equation decreased by at least four orders of magnitude before leveling off. Aerodynamic force coefficients for the entire aircraft and engine mass flow rates were monitored in addition to the residuals to determine if iterative convergence had been reached. A typical simulation was completed in 7,000 iterations, using roughly 1,120 CPU hours. B. Stability-Analysis Simulation Flowfield Results CFD simulations examining the flowfield and boundary-layer stability characteristics of the glove can be categorized into three groups of test points. The first involved a sweep in aircraft AoA from 3.2 to 4.0 in 0.2 increments. The second group investigated changing Mach number, including M = 0.66, M = 0.72, M = 0.75, and M = The third explored the effects of various Reynolds numbers, including Re c = at BL270, Re c = at BL270, and Re c = at BL198. The Reynolds number calculation uses the glove chord at the given span location as its reference length. All groups shared one principal test point, which was defined as M = 0.75, AoA = 3.4, and Re c = at BL270. These conditions were used during the glove OML optimization and represent the sweet spot for the glove design. They will also serve as the initial condition target for the test flight phase of the project. All other test points are copies of the principal test point, excluding the one parameter under investigation. For example, the AoA simulations share M = 0.75 and Re c = at BL270, but vary in AoA. The flowfield results from the principal test point provide early insight into the flow behavior over the glove. The first major finding obtained from the principal test point simulation is the level of spanwise uniformity in pressure distribution across the glove. Obtaining a spanwise-uniform pressure distribution is important in achieving 9

10 consistent boundary-layer stability characteristics across the much of the glove. Figure 9 displays C p results at several span locations. The overall C p behavior is fairly uniform, indicating that the optimization of the glove OML was successful 9. This result is a marked improvement from the previous design, TAMU-05-04, discussed in Belisle et al (1111) and is consistent with the results from Hartshorn et al (12). This plot also shows an accelerating pressure gradient up to roughly 60% x/c on both sides of the glove, which will suppress the growth of T-S waves. Furthermore, it was discovered that there was supercritical flow on the suction side of the glove from roughly 20% - 65% x/c. Figure 9. Glove C p results for principal test point at various span locations. With the principal test point simulation complete, sensitivity to test point parameter changes were investigated, beginning with variations in aircraft AoA. The results from these simulations showed that there is some sensitivity to small aircraft AoA changes. In addition to geometric requirements for the project, a lift coefficient requirement was also given. The C l for the test section was specified to be 0.5 or larger. Because the pressure distribution across the span of the test section varied slightly, the sectional C l also experienced changes. Rather than pick and choose which C l to report based on span location, an average C L over the entire test section was calculated. Table 3, below, displays the results based on aircraft AoA. The AoA = 3.2 and 3.4 simulations come up a bit short of the requirement but are certainly in the ballpark, showing that only a slight increase in AoA is necessary to reach the desired lift coefficient. Table 3. Glove test section lift coefficients for the angle of attack simulations. Angle of Attack Lift Coefficient The test section pressure distribution also experienced changes with variable AoA. Figure 10 displays C p results at BL212, BL234, and BL264. For all sections, the suction side pressure gradient becomes less accelerated and the pressure side becomes more accelerated as aircraft AoA increases. The suction-side C p at BL212 shows a loss in spanwise uniformity and an adverse pressure gradient forward of 60% x/c at AoA = 4.0. Analysis of the glove and wing pressure contours explains this behavior. As shown by Figure 11, a pocket of low pressure near the leading edge of the inboard fairing grows larger with increasing AoA, eventually spilling onto the glove test section. This behavior could destabilize T-S prior to the steep adverse pressure gradient at 60% x/c and cause transition earlier than desired. 10

11 Figure 10. Glove C p comparison for the AoA simulations at a) BL212, b) BL234, and c) BL264. Figure 11. C p contours near the leading edge of the inboard fairing for the AoA simulations at a) 3.2, b) 3.4, c) 3.6, d) 3.8, e)

12 The Mach number simulations also provided valuable information on the sensitivity of the flowfield with changing Mach number. The pressure distribution was altered significantly with relatively small changes in Mach number. The glove design was optimized for M = Figure 12 shows C p results at BL234 for M = 0.66, M = 0.72, M = 0.75, and M = 0.76 at BL234. The critical C p for each Mach number is included to show regions of supercritical flow. Only the M = 0.66 case is completely subsonic. As Mach number decreases, the pressure gradient in the middle portion of the glove flattens out and increased T-S wave growth may occur. Additionally, the near-zero pressure gradient in the middle of the glove should greatly stabilize crossflow, possibly making DRE control more difficult since the SWLFC technique relies on crossflow dominated transition. C p results at other glove span stations behaved similarly. These results illustrate the importance of remaining at an on-design Mach number during the science missions of the flight test program. Figure 12. Glove C p results for the Mach number simulations at BL234. The Reynolds numbers simulations showed very little variation in the test section flowfield results with all other test point parameters held constant. The section C p for the Re c = at BL270 and Re c = at BL198 matched the principal test point (Re c = at BL270) nearly exactly, as illustrated in Figure 13. The boundarylayer stability results instead provide more meaningful information with regard to glove design effectiveness. 12

13 Figure 13. Glove C p results for the Reynolds number simulations at a) BL212, b) BL234, and c) BL264. V. Full Aircraft Boundary-Layer Stability Calculations Boundary-layer stability calculations were performed for the glove using flowfield information obtained from the full-aircraft CFD simulations previously discussed. Key boundary-layer stability information can be gleaned from these calculations, such as the most unstable crossflow (critical) wavelength, possible control wavelengths to use for DRE spacing, neutral point location for DRE placement, and transition location prediction. The NASA code LASTRAC 18 was used to perform all boundary-layer stability calculations. Two laminar-flow requirements were specified for the project. The first focused on the NLF portion of the experiment, requiring a suction-side transition location greater than or equal to 60% x/c and a transition front of at least 0.36 m (14 in) in the spanwise direction for Re c The second focused on the SWLFC portion of the experiment, requiring the suction-side transition location to be moved beyond its NLF location by a factor of 1.5 when using DREs for Re c For example, if the NLF transition location is at 40% x/c, the implementation of DREs must increase this location to 60% x/c. A. Flowfield Data Extraction and Conditioning The first step in performing boundary-layer stability calculations is to extract and condition test section boundary-layer information. To accomplish this, significant planning and the development of several utility codes was required. The method in which LASTRAC performs stability calculations heavily influenced this process. LASTRAC was developed to perform calculations for an infinite-swept-wing geometry. This particular configuration results in constant flow properties in the leading-edge-parallel direction. This means leading-edgeperpendicular flowfield behavior is independent of span location, resulting in unvarying boundary-layer stability characteristics along the span of the wing. The wing glove, however, has a conical-swept-wing geometry that was optimized to obtain conical flow, which is inconsistent with the assumptions that led to the standard leading-edgeperpendicular marching method employed by LASTRAC. While the glove does not achieve perfect spanwise 13

14 uniformity, it at least approximates conical flow. For conical flow, the direction of constant flow properties is along constant-x/c lines, meaning that the marching direction should remain locally perpendicular to these lines to mimic the leading-edge-perpendicular marching method. This marching scheme is not possible in the literal sense, unfortunately, because of the limited test section span. Doing so would result in marching off the test section for starting points near the inboard boundary of the test section. However, this problem is solved by using the constant properties along constant-x/c lines assumption, which makes a marching direction along a constant span location, e.g. BL234, equivalent to a marching direction that is locally perpendicular to constant-x/c lines. Figure 14 illustrates the conical swept-wing-marching method below. The assumptions made at this stage were later investigated to ensure that they were indeed valid. Figure 14. Conical swept wing marching method. Two utility codes were written to help perform the flowfield data extraction and conditioning necessary to complete stability calculations. The first was responsible for assisting with the data extraction from a FLUENT simulation. Using surface mesh information for the glove, the local wall-normal direction was determined for a userspecified span location. This information was in turn written to the FLUENT journal file which, along with userdefined functions created for FLUENT, performed the extraction of boundary-layer data along wall-normal lines. The second code was responsible for conditioning the recently extracted data. The velocity components taken from the CFD simulations were originally given in a global coordinate system. These were transformed into a body-fitted coordinate system, which included wall-normal (y), marching-direction-parallel (x), and marching-directionperpendicular (z) directions as shown above in Figure 14. Once all data was properly conditioned, it was written into a binary mean flow file used by LASTRAC to perform the stability calculations. More detail of this process can be found in Roberts 2012 (19). Mean flow files were created for both the suction and pressure sides for six span locations and for all test points investigated. B. Linear Stability Theory Calculations The boundary-layer stability calculation results presented in this paper were completed using linear stability theory (LST), which neglects non-parallel and nonlinear effects. The effects of surface curvature were not included. Two sets of LST calculations were carried out. The first set investigated stationary crossflow and served as the primary focus because the SWLFC technique is strongly dependent on crossflow characteristics. The second set examined T-S with a wave propagation parallel to the marching path (zero spanwise wavenumber). The Smith Van- Ingen e N method served as the main stability evaluation tool, not only to determine important stability parameters for the SWLFC technique, but to help establish expected transition locations. For crossflow using a highly-polished leading edge, transition was assumed to occur at N = 14. For crossflow using an operationally-realistic painted leading edge, transition was assumed to occur at N = 9. These values are empirically based on prior test flight experience. The limiting N-factor criterion for T-S was set to N = 6. The N-factors should not exceed this level, 14

15 ensuring compatibility with the SWLFC approach, which calls for crossflow-dominated transition. Due to the adverse pressure gradients found on both sides of the test section beyond 60% x/c, it is anticipated that the T-S mechanism will lead to turbulence quickly. As such, laminar flow is not expected beyond 60% x/c. The stability characteristics of the principal test point were the most heavily scrutinized because it represents the primary target for the SWLFC portion of the test flight phase of the experiment. As noted earlier, the first order of business is to note the consistency of the stability behavior across the glove. Large deviations, especially in the center of the test section, would invalidate the conical-swept-wing marching method and signal serious design problems. Figure 15 gives suction-side crossflow N-factor results for span locations of BL212, BL222, BL234, and BL246. Figure 15. Suction-side crossflow N-factor results from principal test point simulation: a) BL212, b) BL222, c) BL234, and d) BL246. A great deal of information can be obtained from the above plots. First, the stability characteristics at all four sections are fairly uniform considering the sensitivity of boundary-layer stability calculations. The important SWLFC parameters, such as candidate control wavelengths, the critical wavelength, and the Branch I neutral point location, are also consistent, which bodes well for DRE control over much of the test section span. The critical wavelength was generally 7 mm. The 3.5 mm wave could be used for control, since it grows to N-factors between 5 and 6 and downstream roughly 15% x/c. The 4 mm wave is another possible candidate. The 7 mm wave consistently begins growing at 0.6% x/c across the entirety of the test section. The DRE array would be positioned at this location to force the subcritical wavelength and subsequently suppress the critical wavelength. The predicted transition locations for both the N = 9 and N = 14 criteria (whose x/c values can be found with the help of the horizontal gray lines in the N-factor plots) were also fairly uniform across the test section. They differed by no more than 6% x/c from BL212 to BL246. All of these findings show that the conical swept wing assumptions made earlier are reasonable. 15

16 While the center portion of the test section returned consistent results, the airfoil sections near the boundaries, BL204 and BL264, experienced larger disturbance growth, causing the predicted transition locations to move much further forward. The SWLFC parameters also experienced some slight changes from those reported from the center span locations. This is not entirely unexpected due to these sections proximity to the test section boundaries, where conical-swept-wing flow would likely be spoiled by the nearby fairings. Stability calculations were completed for the pressure side of the test section as well. These results were primarily used for predicting transition location since implementation of DREs for this side is unlikely. Additionally, T-S results for both sides at all sections were analyzed. The suction side experienced little to no T-S growth as expected due to the favorable pressure gradient back to 60% x/c. The pressure side saw slightly larger T-S growth than the suction side because its gradient wasn t nearly as accelerated. However, the maximum N-factors were typically less than N = 4, with none reaching the N = 6 limit. To better display the predicted transition location due to crossflow, N-factor contour plots for the test section were created. These plots give the location of the transition front and shade the region where laminar flow is expected. Empirical 10 transition wedges emanating from the leading-edge corners of the test section were included, assuming a 10 inboard skew to better match the streamline behavior over a swept wing. Figure 16 shows crossflow transition predictions for both the suction and pressure sides for the principal test points. For the suction side, the N = 9 contour line predicts a transition location of roughly 25% x/c across the middle portion of the glove, leaving ample room to increase laminar flow by a factor of 1.5 through the use of DREs without saturating at the 60% x/c location. This would allow the SWLFC requirement to be met. For the N = 14 contour line, demonstrating DRE effectiveness would be difficult because the transition region is already approaching 60% x/c in the center of the glove, preventing gains in laminar flow to be made. For the pressure side, laminar flow can be achieved naturally anywhere between 32% x/c for N = 9 and 50% x/c for N = 14. Figure 16. Crossflow N-factor contours from the principal test point: a) suction side and b) pressure side. Aircraft AoA = 3.4, M = 0.75, Re c = at BL270. The angle of attack simulation flowfield results showed pressure-gradient sensitivity to changes in aircraft AoA, signaling possible changes in stability behavior. The stability results from these simulations experienced only slight changes in the SWLFC parameters, with the largest difference being the 4 mm wave possibly serving as a better control candidate at the higher AoA s. The predicted transition locations, however, were significantly modified over the investigated AoA range. As noted earlier, the suction-side pressure gradient became less accelerated and pressure-side pressure gradient became more accelerated with increasing aircraft AoA. This behavior leads to crossflow stabilization and T-S destabilization on the suction side, while the opposite occurs on the pressure side. Figure 17 shows how the predicted crossflow transition location changes over the AoA range investigated for this experiment. Transition moved back an additional 10% x/c in the center of the test section for the N = 9 criterion through an increase from AoA = 3.2 to AoA = 3.6. Even larger amounts of laminar flow were obtained through an increase to AoA = 4.0, though the laminar flow region narrowed in the spanwise direction for higher AoAs. 16

17 Figure 17. Suction-side crossflow N-factor contours for the angle of attack simulations: a) 3.2, b) 3.6, and c) 4.0. It should be reiterated that the above plots only consider the crossflow mechanism when determining the expected transition location. The suction side did experience elevated T-S N-factors as aircraft AoA increased, but they typically remained well below the N = 6 limit. However, there was one instance where this was not the case. Earlier, it was shown that a local pressure minimum develops near the inboard boundary of the test section at AoA = 4.0. This flow feature led to strong T-S growth shortly after the local adverse pressure gradient begins, as displayed in Figure 18. While the N = 6 criterion is not exceeded, the nearness to the limit and rapid growth over such a short distance is concerning, especially since T-S has typically been benign in other calculations. This reaffirms that all adverse pressure gradients forward of 60% x/c should be avoided to ensure T-S is not responsible for early transition. Figure 18. Suction-side T-S N-factor results at BL204 for the AoA = 4.0 simulation. The flowfield results from the Mach number simulations showed that the pressure gradient was significantly affected at off-design Mach numbers. Concerns were previously raised about the stabilization of crossflow making it difficult to implement the SWLFC technique due to the large regions of near-zero pressure gradient for the M = 0.66 and M = 0.72 simulations. The stability calculations completed for these test points confirmed that crossflow would indeed be stabilized and showed large increases in predicted laminar flow. However, this comes at a cost of destabilized T-S. For all span locations from the M = 0.66 simulation, the N = 6 limit for T-S was exceeded. The M = 0.72 simulation saw similar stability characteristics, though the T-S N-factors were slightly lower. Even if T-S did 17

18 not cause early transition for these test points, the over-stabilization of crossflow could seriously inhibit the SWLFC technique. Therefore, off-design Mach numbers during the test flight phase of the experiment are not desirable for this particular glove design. The flowfield results from the Reynolds number simulations showed little variation in the glove pressure distribution for varying chord Reynolds number. Stability behavior, however, is greatly affected by Reynolds number, which is why the laminar flow requirements specified for the experiment are directly tied to chord Reynolds number. The three simulations completed represent the limiting cases for the NLF and SWLFC portions of the experiment. The Re c = at BL270 simulation has direct implications on the NLF portion and its laminar flow requirement. The Re c = at BL270 simulation (principal test point) serves as the lower bound to the SWLFC portion of the experimental flight envelope. The Re c = at BL198 simulation serves as the upper bound to the SWLFC portion of the flight envelope and will be used to compare directly against the principal test point to better understand the sensitivity of expected transition for this Reynolds number range. The suction-side N- factor contour plots given in Figure 19 show the predicted amounts of laminar flow for all three simulations. Figure 19. Suction-side crossflow N-factor contours for the Reynolds number simulations: a) Re c = at BL270, b) Re c = at BL270, and c) Re c = at BL198. For the Re c = at BL270 simulation, it appears as though the NLF requirement can be met for N = 14 criterion, but not for the N = 9 criterion. This indicates a polished leading edge will likely be necessary to meet the NLF requirement for this glove design. The amounts of laminar flow obtained through the use of an operationallyrealistic painted leading edge are still encouraging because transition occurs naturally at 50% x/c in the center of the test section. For the SWLFC Reynolds number range, the behavior of note is the change in the amount of laminar flow for the Re c = at BL270 and the Re c = at BL198 simulations. For the center portion of the test section, the transition front only moved forward a few percent x/c across the entire SWLFC Reynolds number range. Larger changes occurred near the test section boundaries, which effectively narrows the laminar flow region. Based on the discussion already given for the principal test point, the framework to meet the SWLFC requirement of increasing laminar flow by a factor of 1.5 is in place and will depend on DRE performance. For the Re c = at BL198 simulation, the SWLFC parameters changed from the principal test point. The critical wavelength and the possible control wavelength decreased to 5 mm and 3 mm respectively and the Branch I neutral point moved forward to 0.1% x/c. Any concerns that may have existed about the suction-side T-S for this simulation due to the increased Reynolds number were relieved by results that showed that T-S was still sufficiently suppressed. VI. Conclusion Early full-aircraft flowfield and boundary-layer stability results indicate that the current glove design, TAMU , will perform as intended, assuming reasonable tolerances on test flight conditions such as aircraft AoA and Mach number. The optimized glove OML generates an acceptable level of pressure spanwise uniformity to produce consistent stability characteristics in the center of the glove test section. Flowfield sensitivity to changes in aircraft AoA and Mach number should be addressed through the test flight planning due to the effect small changes to these parameters have on the test section stability behavior. Initial LST results provided first-order insight into the stability behavior of the glove. The full-aircraft stability calculations trends were similar to the simplified calculations performed during the glove design phase 9. The laminar flow prediction results indicate the two laminar flow 18

19 requirements can be met. Considering the analysis conducted on the current wing glove design, a successful test flight experiment exploring transition delay through the use of DRE technology is well within the realm of possibility. Acknowledgments This work was supported under ViGYAN subrecipient grant C , ATK grant SP , and AFOSR grant A4760. This work is a cooperative effort with NASA Dryden Flight Research Center and NASA Langley Research Center. Technical interactions with the NASA Centers are gratefully acknowledged. The authors also acknowledge the Texas A&M Supercomputing Facility for providing computing resources and ANSYS Support for their assistance in creating FLUENT user defined functions. Both were extremely useful in conducting the research reported in this paper. Lastly, project team members Mike Belisle, Brian Crawford, Aaron Tucker, Matthew Tufts, David West, and Thomas Williams should be recognized for their contributions to this work. References 1 Joslin, R. D., Overview of Laminar Flow Control, NASA Langley Research Center, NASA/TP , Hampton, VA, Oct Thibert, J. J., Reneaux, J., and Schmitt, R. V., ONERA Activities on Drag Reduction, Proceedings of the 17th Congress of the International Council of the Aeronautical Sciences, Sept. 1990, pp Saric, W. S., Carpenter, A. L., and Reed, H. L., Passive Control of Transition in Three-Dimensional Boundary Layers, with Emphasis on Discrete Roughness Elements, Philosophical Transactions of the Royal Society A, 369, April 2011, pp Saric, W. S., Reed, H. L., White E., Stability of 3-D Boundary Layers, Annual Review of Fluid Mechanics 35, , Radeztsky, R. H., Reibert, M. S., and Saric W. S., Leading-Edge Roughness as a Transition Control Mechanism, AIAA Journal, Vol. 37, No. 11, Nov. 1999, pp Saric, W. S., Carrillo, R. B., and Reibert, M. S., Leading-Edge Roughness as a Transition Control Mechanism, AIAA Paper No , Jan Saric, W. S., and Reed, H. L., Crossflow Instabilities Theory and Technology, AIAA Paper No , Jan Carpenter, A. L., Saric, W. S., and Reed, H. L., In-Flight Receptivity Experiments on a 30-Degree Swept-Wing using Micron-Sized Discrete Roughness Elements, AIAA Paper , Jan Belisle, M. J., Roberts, M. W., Williams, T. C., Tufts, M. W., Tucker, A. A., Saric, W. S., and Reed, H. L., A Transonic Laminar-Flow Wing Glove Flight Experiment: Overview and Design Optimization, AIAA Paper, June Belisle, M. J., Neale, T. P., Reed, H. L., and Saric, W. S., Design of a Swept-Wing Laminar Flow Control Experiment for Transonic Aircraft, AIAA Paper , June Belisle, M. J., Roberts, M. W., Tufts, M. W., Tucker, A. A., Williams, T. C., Saric, W. S., and Reed, H. L., Design of the Subsonic Aircraft Roughness Glove Experiment, AIAA Paper , June Hartshorn, F., Belisle, M. J., Reed, H. L., Computational Optimization of a Natural Laminar Flow Experimental Wing Glove, AIAA , Jan Rhodes, R. G., Carpenter, A. L., Reed, H. L., and Saric, W. S., CFD Analysis of Flight-Test Configuration for LFC on Swept Wings, AIAA Paper , Aug Rhodes R. G., Reed, H. L., Saric, W. S., Carpenter, A. L., Neale, T. P., Roughness Receptivity in Swept-Wing Boundary Layers Computations, International Journal of Engineering Systems Modeling and Simulation, Vol. 2, No. 1/2, , March Vassberg, J. C., Tinoco, E. N., Mani, M., Rider, B., Zickuhr, T., Levy, D. W., Brodersen, O. P., Eisfeld, B., Crippa, S., Wahls, R. A., Morrison, J. H., Mavriplis, D. J., Murayam, M., Summary of the Fourth AIAA CFD Drag Prediction Workshop, AIAA Paper , June Oberkampf, W. L., Sindir, M. M., Conlisk, A. T., Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, AIAA G , Jan Menter, F. L., Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, Vol. 32, No. 8, Aug. 1994, pp Chang, C., Langley Stability and Transition Analysis Code (LASTRAC) Version 1.2 User Manual, NASA Langley Research Center, NASA/TM , Hampton, VA, June Roberts, M. W., Computational Evaluation of a Transonic Laminar-Flow Wing Glove Design, M.S Thesis, Aerospace Engineering Department, Texas A&M University,