Novel Aircraft Design
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Engine Modeling for CFD
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Boundary Layer Ingestion (BLI)
PropulsorAirframe Integration as a Way to Improve Aircraft Performance
Overview
Boundary layer ingestion (BLI) has the potential to provide step improvements in fuel consumption and has been proposed for a number of advanced subsonic transport aircraft concepts With BLI, a portion of the airframe's boundary layer is ingested and reenergized by the propulsors. BLI reduces the overall power dissipation in the flowfield, primarily by reducing wasted kinetic energy in the exhaust jet and also by "fillingin" the wake defect, as illustrated in the figure below.
In order to justify the increased complexity of using BLI, it is important to be able to predict the achievable performance gains, and to understand their physical origins: my research aims at doing this.
One complication of BLI is the force accounting for the entire aircraft, since the usual notions of thrust and drag become ambiguous. A better approach is to consider mechanical energy sources and sinks and analyze BLI using power balance [Drela 2009; Hall et al. 2017; Uranga et al. 2018].
In the power balance framework, the entire aerodynamic flowfield of the airframe plus propulsors is included in one analysis that unifies all the power losses on the aircraft. The surface boundary layer losses of the airframe and the propulsive losses of the power plant are directly related to the power (and hence fuel burn) of the propulsor.
The power balance is formulated on a control volume with inner boundary covering the body surface and spanning the propulsor inlet and exit planes, and an outer boundary effectively at infinity.
In level flight, the difference between the total dissipation in the flowfield and the power added is equal to the streamwise force power (net streamwise force times flight velocity). Thus, only the net streamwise force ("drag minus thrust") is needed and remains well defined.
The dissipation can be broken down into surface dissipation occurring in the boundary layers along the aircraft surfaces, wake dissipation in the viscous wakes, vortex dissipation equal to the conventional induced drag power, and jet dissipation in the propulsor jet streams. To counteract these losses, the propulsors add a certain amount of mechanical flow power,
, to the flow. These terms are illustrated in the figure below. Thus, the power balance equation can be written as
where is the net streamwise force, the flight velocity, the rate of climb, and the aircraft weight.
The advantageous effects of BLI for transport aircraft can be classified as follows:
 Reduced propulsor jet dissipation for a given force and therefore increased propulsive efficiency: a lower propulsor power is thus required to obtain the same net streamwise force
 Reduced surface dissipation due to the smaller partially embedded nacelles, that see lower surface velocities
 Reduced wake dissipation due to the propulsors partially elimi nating the fuselage viscous wake
 Reduced weight due to smaller nacelles and smaller engines (from the reduced power requirement), which in turn enables smaller wings, and thus an even lighter aircraft
The first three effects correspond to comparison of flight power requirements for a given airframe operating at the same lift coefficient, and constitute the aerodynamic benefit of BLI. In a design setting, the airframe can be reoptimized to take full advantage of BLI, thus leading to the fourth benefit source: the systemlevel benefit. Experimental tests of the D8 configuration demonstrated an aerodynamic benefit from BLI of more than 8% [Uranga et al. 2017], with a total systemlevel benefit estimated to be close to 19% [Uranga et al. 2014].
References
 A. Uranga, M. Drela, D. Hall, and E. Greitzer, "Analysis of the Aerodynamic Benefit from Boundary Layer Ingestion for Transport Aircraft", AIAA Journal, Vol.56, No. 11, pp. 42714281, 2018. doi: 10.2514/1.J056781
 A. Uranga, M. Drela, E.M. Greitzer, D.K. Hall, N.A. Titchener, M.K. Lieu, N.M. Siu, C. Casses, A.C. Huang, G.M. Gatlin, and J.A. Hannon, "Boundary Layer Ingestion Benefit of the D8 Transport Aircraft", AIAA Journal, Vol. 55, No. 11, pp. 3693–3708, 2017. doi: 10.2514/1.J055755
 D.K. Hall, A.C. Huang, A. Uranga, E.M. Greitzer, M. Drela, and S. Sato, "Boundary Layer Ingestion Propulsion Benefit for Transport Aircraft", Journal of Propulsion and Power, Vol. 33, No. 5, pp. 1118–1129, 2017. doi: 10.2514/1.B36321
 M. Drela, "Power Balance in Aerodynamic Flows", AIAA Journal, Vol. 47, No. 7, pp. 1761–1771, 2009.
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MIT/NASA N+3 Program
Aircraft and Technology Concepts for an N+3 Subsonic Transport
Overview
To address the challenges posed by the projected increase in aviation demand and the growing environmental concerns, NASA put forward a multiphase program starting in 2008 aimed at the development of commercial transport aircraft that could provide step improvements in performance. Named N+3 to refer to the targeted three generations ahead of the current fleet, the program focused on aircraft that could enter into service in the 2025–2035 timeframe.
A team from MIT, Aurora Flight Science, and Pratt & Whitney was initially formed to respond to the solicitation, and was later (in Phase 3) joined by United Technologies Research Center (UTRC), the University of Michigan, and the University of Southern California (USC).
In Phase 1 of the N+3 program (20082010), the MITled team examined a number of technologies and aircraft concepts, including a 180passenger D8 "double bubble" aircraft in the Boeing 737800 or Airbus 320 class, which was predicted to provide a reduction of almost 70% fuel burn compared to the reference 737800 aircraft. The recognition at the end of Phase 1 was that the D8 held considerable potential, and the two areas with highest uncertainty were identified: the use of boundary layer ingesting (BLI) propulsors and the small core engines needed to drive these.
This D8 concept was selected by NASA for further development in a Phase 2 project (20102015) with the goal of quantifying the benefit of boundary layer ingestion via a combined experimental and computational effort, and of advancing the readiness level of the highlyefficient, high pressure ratio small core engines that the D8 called for. A major conclusion from the Phase 2 program is that BLI is a viable technology for reducing fuel burn and emissions of commercial subsonic transports. BLI was shown to provide an aerodynamic benefit that amounts to an 8% reduction in power required at cruise, as measured in wind tunnel tests at the NASA Langley 14– by 22–Foot Subsonic Tunnel. Furthermore, an alternative architecture, nonconcentric, reversedcore engine was conceptually designed for the D8, which holds considerable promise for future transport aircraft of all types. The Phase 2 work was done in close collaboration with NASA.
Phase 3 (20152017) included conceptuallevel studies to more precisely determine the fuelburn benefit of the Dseries configuration relative to a conventional tubeandwing aircraft and its uncertainty. Performance gains related to the use of N+3 technology level assumptions were determined separately from the configuration benefits, as well as the sensitivities to mission range and payload. The design of a transonic D8 aircraft using MDO with coupled aerodynamicsstructuralpropulsion was also performed, which included definition of the aerodynamic outermoldlines and engine characteristics, at a level suitable for experimental and CFD transonic studies.
You will find here a summary of the work. For more information, see the publications listed for each Phase.
Phase 1 (20082010)
 E. Greitzer, P. Bonnefoy, E. De la Rosa Blanco, C. Dorbian, M. Drela, D. Hall, R. Hansman, J. Hileman, R. Liebeck, J. Lovergren, P. Mody, J. Pertuze, S. Sato, Z. Spakovszky, C. Tan, J. Hollman, J. Duda, N. Fitzgerald, J. Houghton, J. Kerrebrock, G. Kiwada, D. Kordonowy, J. Parrish, J. Tylko, and D. Wen, "N+3 Aircraft Concept Designs and Trade Studies, Final Report", NASA CR 2010216794, 2010.
 M. Drela, "Power Balance in Aerodynamic Flows", AIAA Journal, Vol. 47, No. 7, pp. 1761– 1771, 2009.
Phase 2 (20102015)
Technology Lead: Alejandra Uranga (formerly MIT)
Chief Engineer: Mark Drela (MIT)
Participating organizations: MIT, Aurora Flight Sciences, Pratt & Whitney,
Abstract
The aerodynamic benefit of BLI at cruise was quantified to be 8.6% at fixed nozzle area, through a backtoback comparison of nonBLI and BLI versions of the D8, which included lowspeed tests of 1:11 scale powered models in the NASA Langley 14– by 22–Foot Subsonic Tunnel. This represents the first measurement of BLI performance improvements for a realistic aircraft configuration. A novel engine architecture with a nonconcentric, reverseflow arrangement of the core and fan sections was conceived to satisfy the FAA 1in20 engine failure rule for the D8 aircraft's integrated propulsion system with sidebyside engines. The BLI benefit results, coupled with the innovative engine design, give evidence that aircraft using BLI can provide a viable path for step improvements in fuel efficiency of subsonic transports.
References
 A. Uranga, M. Drela, E. Greitzer, C. Casses, A. DiOrio, A. Espitia, A. Grasch, D. Hall, A. Huang, M. Lieu, S. Sato, N. Siu, C. Tan, N. Titchener, E. van Dam, J. Hollman, D. Kordonowy, R. Opperman, J. Chambers, B. Smith, E. Pliakas, A. Cardona, S. Giblin, D. Campbell, W. Lord, and G. Suciu, "Aircraft and Technology Concepts for an N+3 Subsonic Transport, Phase 2 Final Report", GTL Report Series 2, Report No. 2001, Gas Turbine Laboratory, Massachusetts Institute of Technology, 2018.
 A. Uranga, M. Drela, E. Greitzer, D. Hall, N. Titchener, M. Lieu, N. Siu, C. Casses, A. Huang, G. Gatlin, J. Hannon, "Boundary Layer Ingestion Benefit of the D8 Transport Aircraft", AIAA Journal, Vol. 55, No. 11, pp. 3693–3708, 2017. doi: 10.2514/1.J055755
 A. Uranga, M. Drela, D. Hall, and E. Greitzer, "Analysis of the Aerodynamic Benefit from Boundary Layer Ingestion for Transport Aircraft", AIAA Journal, in press, 2018.
 D. Hall, A. Huang, A. Uranga, E. Greitzer, M. Drela, and S. Sato, "Boundary Layer Ingestion Propulsion Benefit for Transport Aircraft", Journal of Propulsion and Power, Vol. 33, No. 5, pp. 1118–1129, 2017. doi: 10.2514/1.B36321
 M. Drela, "Development of the D8 transport configuration", AIAA 20113970, 29th AIAA Applied Aerodynamics Conference, Honolulu, HI, , 2730 June 2011.
 M. Lieu, A. Uranga, M. Drela, and E. Greitzer, "Rapid Flow Surveys via Rotating Rake System and Use in Powered Wind Tunnel Models" , AIAA 20142801, 30th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Atlanta, Georgia, 1620 June 2014. doi: 10.2514/6.20142801
 N. Siu, N. Titchener, C. Casses, A. Huang, A. Uranga, M. Drela, and E. Greitzer, "Evaluating Propulsor Mechanical Flow Power in Powered Aircraft Wind Tunnel Experiments" , AIAA20142566, 32nd AIAA Applied Aerodynamics Conference, Atlanta, Georgia, 1620 June 2014. doi: 10.2514/6.20142566
 A. Uranga, M. Drela, E. Greitzer, N. Titchener, M. Lieu, N. Siu, A. Huang, G. Gatlin, and J. Hannon, "Preliminary Experimental Assessment of the Boundary Layer Ingestion Benefit for the D8 Aircraft" , AIAA20140906, 52nd AIAA Aerospace Sciences Meeting, SciTech 2014, National Harbor, Maryland, 1317 Jan. 2014. doi: 10.2514/6.20140906
 S. Pandya, A. Huang, A. Espitia, and A. Uranga, A., "Computational Assessment of the Boundary Layer Ingesting Nacelle Design of the D8 Aircraft" AIAA20140907, 52nd AIAA Aerospace Sciences Meeting, Science and Technology Forum and Exposition, SciTech2014, National Harbor, Maryland, 1317 Jan. 2014. doi: 10.2514/6.20140907
Phase 3 (20152017)
coPI: Ed Greitzer (MIT)
Participating organizations: Massachusetts Institute of Technology, University of Southern California, United Technologies Research Center, Pratt & Whitney, University of Michigan
Abstract
Through conceptuallevel studies, we determined the fuelburn benefit of the Dseries configuration relative to a conventional tubeandwing aircraft and its uncertainty. This benefit amounts to between 17.6% and 23.1% lower fuel burn depending of how the comparison is made. It is present in spite of, and is much larger than, pessimistic fan performance penalties resulting from boundary layer ingestion (BLI) as determined by analysis of fan efficiency losses and weight gains.
Multidisciplinary design optimization (MDO) was used to design a transonic D8 via aerostructural optimization with a weakly coupled propulsion system. The outcome is a plausible design, at a level of detail suitable for CFD study or wind tunnel experiments, and comprised of outermold lines (including propulsor integration), major structural elements, and designpoint engine characteristics for cruise speeds of Mach 0.72 and Mach 0.78. This preliminary highfidelity optimization of the aft fuselage geometry highlight the complexities of integrated propulsion modeling, design, and optimization.
Definitions
 Performance Metric: PayloadRange Fuel Consumption, PRFC: defined as the fuel energy consumed divided by the product of payload weight and range; nondimensionless number quantifying fuel energy consumed relative to the mission productivity (payload times range)

Aircraft
 Conventional configuration: tubeandwing aircraft with a with circular fuselage crosssection, conventional empennage, and two engines mounted under the wings

Dseries configuration: aircraft with a doublebubble lifting fuselage, and two BLI engines mounted on the top aft fuselage under a pitail
 D8: Midrange Dseries aircraft transporting 180 passenger over a range of 3,000 nm
 D12: Longrange Dseries aircraft transporting 450 passengers over range of 7,500 nm
All aircraft considered are singleclass with only economy seats. The payload weight is set by multiplying the number of passengers by a per passenger+baggage weight of 215 lb.

Missions

Midrange: 737class mission of 180 passengers (38,700 lb payload) transported over 3,000 nm range
 Eco or e: Midrange aircraft cruising at Mach 0.72
 Speed or s: Midrange aircraft cruising at Mach 0.78
 Longrange: 777class mission of 450 passengers (96,750 lb payload) transported over 7,500 nm range with cruise Mach number of 0.84

Midrange: 737class mission of 180 passengers (38,700 lb payload) transported over 3,000 nm range

Technologies
 Baseline technology: technology level used on the majority of aircraft flying in 2010. It is characterized by the use of primarily aluminum materials, and engines of the type of a CFM56 (when considering midrange mission) or GE90 (when considering long range missions)
 N+3: technology or aircraft that is ready for entry into service in 2035. It is characterized by the use of primarily composite materials and advanced engines. The specific characteristics of such an engine will be defined in the body of this report

Mission Technology Cruise Speed Range Payload MidRange Eco 8.2e Baseline Mach 0.72 3,000 nmi 180 PAX (38,700 lb) 8.6s N+3 MidRange Speed 8.2s Baseline Mach 0.78 3,000 nmi 180 PAX (38,700 lb) 8.6s N+3 Long Range 12.2 Baseline Mach 0.84 7,500 nmi 450 PAX (96,750 lb) 12.6 N+3
Conceptual Study Results
References
 A. Uranga, E.M. Greitzer, M. Drela, D.K. Hall, Y. Chen, S. Ochs, G. Tillman, D. Voytovych, W. Lord, J.R.R.A. Martins, C.A. Mader, and G.K.W. Kenway, "Transonic D8 Performance and Design  Aircraft and Technology Concepts for an N+3 Subsonic Transport, Phase 3 Final Report", NASA CR, to appear, 2018.
 C.A. Mader, G.K. Kenway, J. Martins, and A. Uranga, "Aerostructural Optimization of the D8 Wing with Varying Cruise Mach Numbers", AIAA 20174436, AIAA Aviation 2017, 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, 2017.
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D8 DoubleBubble Aircraft
Aircraft Concept Overview
Overview
The D8 "doublebubble" aircraft, named for its characteristic fuselage crosssection,
is a 180passenger, 3 000 nm range transport in the Boeing 737 or Airbus A320 aircraft class.
This MITdesigned aircraft concept is characterized by a wide twinaisle lifting fuselage which enables the use of smaller, lighter wings and a pitail empennage with the horizontal tail supported by twin vertical tails. The fuselage nose shape provides a noseup pitching moment that reduces the trimming tail downforce in cruise and further shrinks both the wing and horizontal tail areas. A lowsweep wing that contributes to a lighter structure is made possible by a cruise speed of Mach 0.72, compared to around Mach 0.78 for a conventional tubeandwing aircraft in the same class.
A major feature of the D8 configuration is the use of boundary layer ingestion (BLI): the engines are flushmounted on the top rear of the fuselage, and ingest approximately 13% of the total airframe viscous dissipation (or roughly 40% of the fuselage boundary layer), with the BLI ingestion fractions given as based on boundary layer kinetic energy defect. The fuselage performs much of the diffusion and flow alignment into the fans, which would otherwise be achieved by the nacelle. The D8 nacelles are thus smaller than for conventional podded engines, saving weight and reducing external losses.
The D8 was first designed by M. Drela during MIT's NASAfunded Phase 1 N+3 project, and later refined during Phases 2 (lowspeed geometry and engine integration lines) and Phase 3 (highspeed outermoldline). The first D8 studies during the N+3 Phase 1 project employed three engines. Switching to two engines results in a slight performance decrease but addresses cost and maintenance concerns, and so a twinengine installation was chosen early during the N+3 Phase 2 project.
After completion of the 3 phases in the NASAfunded N+3 project at MIT, the D8 was further developed by Aurora Flight Sciences, now a Boeing Company.
References
 Drela, M.: "Power Balance in Aerodynamic Flows". AIAA Journal, Vol. 47, No. 7, pp. 1761– 1771, 2009.
 Greitzer, E. M.; Bonnefoy, P.; De la Rosa Blanco, E.; Dorbian, C.; Drela, M.; Hall, D.; Hans man, R.; Hileman, J.; Liebeck, R.; Lovergren, J.; Mody, P.; Pertuze, J.; Sato, S.; Spakovszky, Z.; Tan, C.; Hollman, J.; Duda, J.; Fitzgerald, N.; Houghton, J.; Kerrebrock, J.; Kiwada, G.; Kordonowy, D.; Parrish, J.; Tylko, J.; and Wen, E.: "N+3 Aircraft Concept Designs and Trade Studies, Final Report", NASA CR 2010216794, 2010.
 Uranga, A.; Drela, M.; Greitzer, E.; Casses, C.; DiOrio, A.; Espitia, A.; Grasch, A.; Hall, D.; Huang, A.; Lieu, M. K.; Sato, S.; Siu, N.; Tan, C.; Titchener, N.; van Dam, E.; Hollman, J.; Kordonowy, D.; Opperman, R.; Chambers, J.; Smith, B.; Pliakas, E.; Cardona, A.; Giblin, S.; Campbell, D.; Lord, W.; and Suciu, G.: "Aircraft and Technology Concepts for an N+3 Subsonic Transport, Phase 2 Final Report". GTL Report Series 2, Report No. 2001, Gas Turbine Laboratory, Massachusetts Institute of Technology, 2018.
 Uranga, A., Drela, M., Greitzer, E., Titchener, N., Lieu, M., Siu, N., Huang, A., Gatlin, G., and Hannon, J., "Preliminary Experimental Assessment of the Boundary Layer Ingestion Benefit for the D8 Aircraft" , AIAA20140906, 52nd AIAA Aerospace Sciences Meeting, SciTech 2014, National Harbor, Maryland, 1317 Jan. 2014. doi: 10.2514/6.20140906
 A. Uranga, M. Drela, E. Greitzer, D. Hall, N. Titchener, M. Lieu, N. Siu, C. Casses, A. Huang, G. Gatlin, J. Hannon, "Boundary Layer Ingestion Benefit of the D8 Transport Aircraft", AIAA Journal, Vol. 55, No. 11, pp. 3693–3708, 2017. doi: 10.2514/1.J055755
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Transition at Low Reynolds Numbers (PhD Thesis Work)
Investigation of transition to turbulence at low Reynolds numbers using Implicit Large Eddy Simulations with a Discontinuous Galerkin method
Overview
My PhD research involved the use of highorder Discontinuous Galerkin methods for the simulation of transition to turbulence in flows at low and moderate Reynolds numbers. My thesis work was supervised by Jaime Peraire and Mark Drela of MIT, and I worked closely with PerOlof Persson of UC Berkeley.
You will find here a summary of the work. For more information, see the following Publications:

A. Uranga,
"Investigation of Transition to Turbulence at Low Reynolds Numbers Using Implicit Large Eddy Simulations with a Discontinuous Galerkin Method"
,
PhD thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA, Sept. 2010 (degree date: Feb. 2011).
 A. Uranga, P.O. Persson, M. Drela, and J. Peraire, "Preliminary Investigation Into the Effects of CrossFlow on Low Reynolds Number Transition", 20th AIAA Computational Fluid Dynamics Conference, AIAA20113558, Honolulu, Hawaii, June 2730, 2011.
 A. Uranga, P.O. Persson, M. Drela, and J. Peraire, "Implicit Large Eddy Simulation of transition to turbulence at low Reynolds numbers using a Discontinuous Galerkin method", International Journal for Numerical Methods in Engineering, Vol. 86, 2011.
 A. Uranga, P.O. Persson, M. Drela, and J. Peraire, "Implicit Large Eddy Simulation of transitional flows over airfoils and wings", 19th AIAA Computational Fluid Dynamics Conference, AIAA20094131, San Antonio, Texas, June 2225, 2009.
Abstract
This work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence. In addition to being one of the first Implicit Large Eddy Simulation studies using a highorder Discontinuous Galerkin method, unique attention is given to the boundary layer characteristics thus contribut ing to the understanding of low Reynolds number flows and the related separation induced transition. Furthermore, a preliminary transition model suitable for such flows is introduced and its underlying concept proven valid.
The flow around an SD7003 infinite wing at an angle of attack of 4 degrees is first con sidered at Reynolds numbers of 10,000, 22,000, and 60,000. At the lowest Reynolds number studied, the flow remains laminar and two dimensional with a periodic vor tex shedding. For higher Reynolds numbers, the flow is highly unsteady and exhibits a separation bubble on the upper surface over which flow transitions to turbulence. TollmienSchlichting waves are observed in the boundary layer upstream of separation, and their streamwise amplification factor shows they are responsible for transition.
The major effects of crossflow on low Reynolds number transition are studied by comparing the flows over the same infinite wing at different sweep angles. Projecting the results along a common twodimensional equivalent direction, it is established that the crossflow cannot be decoupled from the streamwise evolution at intermediate sweep angles due to strong nonlinear interactions that take place after the laminar boundary layer separates. Hence, for separationinduced transition at low Reynolds numbers, it is not possible to treat streamwise and crossflow instabilities indepen dently for wings with sweep angles between about 10◦ and 40◦, and predicting the mixed transition cannot be reduced to treating the disturbances of each component separately. An important presumption to be adopted in the study of unsteady flows for MAVs and animal locomotion is thus that the type of transition (TS dominated, crossflow dominated, or mixed) is a priori unknown as soon as the flow is slightly misaligned with the wing's chord.
Numerical Method
The compressible, unsteady, NavierStokes equations are solved using a highorder Discontinuous Galerkin (DG) method. The inviscid terms of the numerical fluxes are evaluated with a Roe solver [9], while viscous terms are treated using the Compact Discontinuous Galerkin (CDG) method [7]. The later is a compact method that results in a sparser connectivity matrix than the alternative methods such as the BR2 method [2] and the Local Discontinuous Galerkin (LDG) method [3].
Time integration is performed using the thirdorder accurate diagonal implicit RungeKutta (DIRK) scheme [1]. The nonlinear system of equations is solved using Newton's method with a blockILU/multigrid preconditioned Conjugate Gradient Squared (CGS) solver for the each linear iteration [8].
Following the implicit Large Eddy Simulation (ILES) approach, the fully (unfiltered) compressible NavierStokes equations are solved; the unresolved small eddies are accounted for by means of the numerical dissipation, and no subgridscale model is employed.
Problem Setup
The flow aroung a rectangular wing with an SD7003 airfoil profile is considered, at an angle of attack of 4 degrees, and at Reynolds numbers of 10,000 and 60,000.
The freestream Mach number is set to 0.2, which is low enough that the flow is fundamentally incompressible but high enough to improve numerical stability. The fluid is air with a Prandtl number of 0.72 and specific heat ratio of 1.4, and the kinematic viscosity is assumed constant.
The axes are setup as shown in the figure, with x being the chordwise direction (with the leadingedge at x=0), y the spanwise direction, and z is vertically up. The wing spantochord ratio is set to 0.2, following the findings of Galbraith and Visbal [5].
Extensive experimental data is available for comparison [6], as well as numerical simulations [5]. 

Computational Grid
The computational domain has periodic boundary conditions along the spanwise direction, in order to simulate an infinite wing. The wing's surface is represented by a nonslip, adiabatic, boundary condition, while a fullstate type boundary condition is imposed at the farfield of the computational domain.
The computational domain extends 4.3 chord lengths upstream of the wing's leading edge, 5.9 chord lengths above the wing's leading edge line, 6.0 chord lengths below the wing's leading edge line, and 6.43 chord lengths downstream of the wing's trailing edge. Thus, if we denote by c the chord length, the domain spans on the range [4.3c , 7.4c] x [0 , 0.2c] x [6.0c , 5.9c] along the chordwise, spanwise, and vertical directions, respectively.
The results that follow where obtained on a computational grid with 52,800 tetrahedral elements and 1,056,000 degreesoffreedom. Thirdorder polynomials are used, thus resulting in a fourthorder accurate method in space. The following images show the computational grid on a planar cut along the spanwise direction. 

Results
At a Reynolds number of 10,000 the flow is found to be fundamentally twodimensional with little variation along the spanwise direction and closetoperiodic vortex shedding.
On the contrary, at a Reynolds number of 60,000, threedimensional structures are present as made visible by contours of vorticity or qcriterion. With a fourthorder method, a relatively coarse mesh with one million degreesoffreedom is able to accurately capture the transition location, the position of separation and reattachment, as well as the average pressure and skin friction coefficient profiles along the foil. The pressure and skin friction coefficients can be seen in the figures below; comparison curves with the data by Galbraith and Visbal [5] and with XFoil [4] are also shown.
Temporal animations

Spanwise vorticity at the wing's middleplane at Reynolds 10,000

Spanwise vorticity at the wing's middleplane at Reynolds 60,000

Isosurfaces of qcriterion at Reynolds 10,000

Isosurfaces of qcriterion at Reynolds 60,000

Isosurfaces of spanwise vorticity at Reynolds 60,000

Streamlines at Reynolds 60,000

Fluctuations in pressure coefficient (acoustic field) at Reynolds 60,000
References
[1] R. Alexander, "Diagonally Implicit RungeKutta methods for stiff O.D.E.'s", SIAM J. Numer. Anal., Vol. 14, No. 6, pp. 10061021, 1978.
[2] F. Bassi and S. Rebay, "A highorder accurate discontinuous finite element method for the numerical solution of the compressible NavierStokes equations", J. Comput. Phys., Vol. 131, pp. 267279, 1997.
[3] B. Cockburn and C.W. Shu, "The local discontinuous Galerkin method for timedependent convectiondiffusion systems, SIAM J. Numer. Anal., Vol. 35, No. 6, pp. 24402463, 1998.
[4] M. Drela, XFOIL Users Guide, Version 6.94, MIT Aeronautics and Astronautics Department, 2002.
[5] M. Galbraith and M. Visbal, "Implicit Large Eddy Simulation of low Reynolds number flow past the SD7003 airfoil", 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA paper 2008225, Jan. 2008.
[6] M. Ol, B. McAuliffe, E. Hanff, U. Scholz, and C. Kahler, "Comparison of laminar separation bubble measurements on a low Reynolds number airfoil in three Facilities", 35th AIAA Fluid Dynamics Conference and Exhibit, Toronto, Ontario, Canada, AIAA paper 20055149, June 2005.
[7] J. Peraire and P.O. Persson, "The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems", SIAM J. Sci. Comput., Vol. 30, No. 4, pp. 18061824, 2008.
[8] P.O. Persson and J. Peraire, " An efficient low memory implicit Discontinuous Galerkin algorithm for time dependent problems", 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, AIAA paper 20060113, Jan. 2006.
[9] P.L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes", J. Comput. Phys., 43, 1981.
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