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					Hypersonic Vehicle
Systems Integration
Vehicle Aerodynamic Analysis

     12 September, 2007

        Dr. Kevin G. Bowcutt
      Senior Technical Fellow
    Chief Scientist of Hypersonics
      Boeing Phantom Works



   Hypersonic Educational Initiative
  Conceptual Design Aerodynamic Analysis
• Distinct physics in different flight regimes
    –   Takeoff and subsonic
    –   Transonic
    –   Supersonic
    –   Hypersonic
• Pressure and friction drag contributions
    – Pressure: flow separation, plus wave drag associated with local or
      global supersonic flow
    – Friction: laminar and turbulent - boundary layer transition determines
      the extent of each
• Wing (if required) must be sized for takeoff lift requirement
    – Max angle of attack limited by tail scrape (~ 14-degrees typical)




                     Hypersonic Educational Initiative
   Conceptual Design Aerodynamic Analysis

• Entire aero database can be defined by calculating or
  measuring, as functions of Mach number
   – Vehicle lift-curve-slope
   – Zero-lift or minimum drag (plus maybe CL at minimum drag)
        For contribution from friction drag, must also determine as a
         function of Reynolds number if trajectory to be varied or optimized
   – Drag polar quadratic coefficient (or L/D-max)




                     Hypersonic Educational Initiative
Drivers of Takeoff Aerodynamic Performance

 • Body lift

    – Linear and nonlinear

 • Wing size and lift

    – Possible use of high lift devices, such as flaps

 • Control power for rotation & high-AoA trim

 • Aerodynamic ground effects


               Hypersonic Educational Initiative
  Elements of Subsonic Wing and Body Lift


• Wing / body camber

• Lift system aspect ratio

• Vortex lift

• Ground effects
   – Powered and un-powered




                Hypersonic Educational Initiative
         Linear Contributions to Subsonic
                 Wing or Body Lift
• Thickness effects
   – Increases section C slightly
• Camber effects
   – Shifts lift curve slope either up or down
   – Downward shift for negative body camber common for
     hypersonic vehicles
• Aspect ratio effects (from Nicolai, Ref. 5)
                           2AR
   CL =
             2+      4 + AR22 (1 + tan2 / 2)
         AR = b2 / Splan
         =     1 – M2
          = Sweep angle of maximum thickness line
                    Hypersonic Educational Initiative
       Non-linear Contribution to Subsonic Lift
• For highly swept, low aspect ratio slender bodies,
  leading edge separation can produce large non-linear lift
  contribution
                                                          Secondary Vortex      Primary Vortex


                                                                a
Rectangular Wing   Delta Wing       Body of Revolution
       a                 b                  c                                   -p


                                                                b

                                                                                           y

                                                                    CL   Nonlinear Part
      Vortex Configuration Past Slender Bodies
      From Nicolai [5]
                                                                c
                                                                                 Linear Part

                                                                                     AoA

                                                         From Newsome and Kandil [6]
                             Hypersonic Educational Initiative
          Non-linear Vortex Lift on Rectangular
                    and Delta Wings                                            0.6
                                                                              CL         A=I/5
                                                                                                                 c
                                                                                                                 b
                                                                                                                 a
                                                                               0.4

                                                                               0.2

• Low aspect ratio rectangular                                                   0
                                                                                     0     5° 10° 15°  20° 25°

  wings with stable leading edge                                                         Exp. Flachsbart (1932)
                                                                                         Thin Plate
                                                                                         Exp. Prandtl - Betz (1920)
  separation                                                                             Thick Wing               c
                                                                               1.0                                b
                                                                             CL          A=I                      a
                                       3/2 (Curve “c” on plot)
                                                                               0.8

   – Thin Wing: CL =     AR  +                                               0.6
                      2                2
                                        2 (Curve “a” on plot)                0.4

   – Thick Wing: CL =    AR  +                                               0.2
                       2                2
                                                                                     0     5° 10° 15° 20° 25°
                                                                                                 - o
• Thin delta wings                                         20
                                                                 Overall lift of rectangular wings of small aspect ratio

                                             1.7                 Experiments                   s/

     CN / (s / )2 = 2 / (s / ) + 4.9
                                                                   Brown & Michael (1954)       0.088
                                                                   Fink & Taylor (1955)         0.18
                                           s/                     Peckham (1958)               0.25
                                                                   Marsden, et al (1958)        0.36
                                                          2 10
            s = b/2 = wing half-span                  s
                                                 CN / 
                                                                                                            2
                                                                                                                  
                                                                                                                 s/
             = wing root-chord
                                                            0                          
                                                                                0.5           1.0                     1.5
                                                                                     s/
                                                                      Normal forces on slender delta wings
                                  From Küchemann [7]

                            Hypersonic Educational Initiative
Angle of Attack Limits for Low Speed Flight
                  Vortex Contact
                  or Asymmetry
         40



         30
                                                     Vortex Breakdown
Angle
  of
Attack   20             Complete Recovery
(Deg)                    of Leading Edge
                            Suction as
                          Normal Force
         10
                                                                         2D Bubble
                                                                         Bursting

              0      0.5         1.0     1.5      2.0        2.5 ~ AR

                           80            70               60 ~  (Deg)

                                From Page and Welge [8]

                       Hypersonic Educational Initiative
           Powered Ground Effects
• Engine flow for vehicles with bottom-mounted
  engines can increase or decrease lift when in
  close proximity to the ground
  – Venturi effect and / or supersonic overexpansion
    of engine flow may play roles in phenomenon
  – Effect a function of distance from ground and
    angle of attack

• Testing was conducted at NASA Langley on a
  generic NASP model to quantify effects



              Hypersonic Educational Initiative
    Powered Ground Effects Model Details

                                                                                      24.00

             75°

                      43.58
                                                112.89

                                                Air Sting                 Moment
                                                                          Reference
                              Balance Fairing                    37.5°
                                                                          Center



                                                                                      12.00
                                10°                                 14°


                                                              Ground Height
                     Engine Simulators                        Reference Point
                          55.58                   18.00              39.31

LBODY = 112.89 in.
b     = 24.0 in.
c     = 91.10 in.
Sref = 15.183 ft2
h    = Distance From Cowl to Ground Plane
                                                     Courtesy of Greg Gatlin, NASA Langley

                              Hypersonic Educational Initiative
       Ground Effects for Variations in Thrust
      Coefficient at 12-Degrees Angle of Attack
                        Static Thrust
                CT =
                           q Sref
     0.20
                                                                         CT     q , psf
     0.15                                                                 0          40
                                                                          0.2        40
Cm




     0.10                                                                 0.4        40
                                                                          0.6        26
     0.05                                                                 0.8        20

        0                                                     0.2
      0.3
                                                                0
      0.2
                                                              -0.2
      0.1

                                                         CD
                                                              -0.4
CL




       0
     -0.1                                                     -0.6
                       Approximate Wheel
     -0.2              Touchdown Height
                                                              -0.8
                                                                     0   1.0         2.0    3.0
     -0.3                                                                      h/b
            0          1.0         2.0      3.0
                             h/b
                Large thrust coefficients result in adverse                    Courtesy of Greg Gatlin,
                 ground effects (i.e., suction) at take-off                     NASA Langley

                                         Hypersonic Educational Initiative
 Ground Effects for Variations in Angle of Attack at
0.4 Thrust Coefficient and 40 psf Dynamic Pressure
       0.20

       0.15
                                                                          , deg
  Cm




       0.10                                                                8
                                                                           10
       0.05                                                                12
                                                                           13
          0
        0.3                                                                14

        0.2
                                                         0.1
        0.1
                                                           0
  CL




            0

                                                    CD
                                                         -0.1
       -0.1
                                                         -0.2
       -0.2
                                                         -0.3
                                                                0   1.0      2.0       3.0
       -0.3                                                               h/b
                0    1.0     2.0     3.0
                         h/b
        •       Powered ground effects increase lift at large angles        Courtesy of Greg Gatlin,
                of attack and decrease lift at low angles of attack         NASA Langley

                                   Hypersonic Educational Initiative
          Parasite Drag and Drag Due to Lift
• Parasite (zero-lift) drag
    – Pressure drag due to flow separation and flow leakage
    – Skin friction (laminar and turbulent)
    – Calibrate based on historical data if available
• Drag due to lift (essentially quadratic in all flight regimes)

       CD  CDmin  K (CL  CLmindrag )2
       Assume that C Lm indrag  0, then C Dm in  C D0 (zero - lift drag)
       Then L / D  C L / C D  C L /(C D0  KC L )
                                                2
                                                                                                        (1)
       For ( L / D) m ax, differentiate L / D equation with respect toC L and set to zero, then solve for K
        K  C D0 / C L at ( L / D) m ax
                      2


       Substituting into (1), C D  2C D0 at ( L / D) m ax                                             (2)
       Then, ( L / D) 2 ax  (C L / C D ) 2 at ( L / D) m ax
                      m

       Substituting (1) and (2) into above for C L and C D , respectively, and then solving for K
       K  1/[4CD0 ( L / D) 2 ax]
                            m

       Thereforeneed to determine C D0 and ( L / D) m ax


                                 Hypersonic Educational Initiative
Calculating Drag Polar for Non-Symmetric Lifting
Surfaces When CL at Minimum Drag is Non-Zero
• Generally, lifting surfaces that are not top-to-bottom symmetric will not
  have zero lift at minimum drag
     C D  C Dm in  K (C L  C Lm inD ) 2  C Dm in  KC L m in D  2 KC Lm inD C L  KC L
                                                           2                                 2

                                                                                                                      CD
     Set a  C Dm in  KC L m in D
                          2


           b  2 KC Lm inD
           cK
     Then C D  a  bCL  cCL
                            2


     So, if aero analysis of lift and drag is performedat three AOA points, then one can fit an exact parabola
     through those three points, and K , C Lm inD , and C Dm in can be obtained from the parabola coefficients                           CD min
     K c
                                                                                                                                                   CL
     C Lm inD  b /(2 K ), and
                                                                                                                             CL min-
     C Dm in  a  KC L m in D
                      2

                                                                                                                             D
     Then, (L/D)m ax can be obtained by dividing C L by C D , differentiating with respect toC L and setting the result to zero
     L / D  C L /C D  C L /(a  bCL  cC L ), and
                                           2


     d (C L /C D ) (a  bCL  cC L ) - C L (b  2cC L )
                                 2
                                                                            Note: If CL min-D is very small, then it could be neglected
                                                       0
        dCL               (a  bCL  cC L ) 2
                                            2
                                                                            in the quadratic CD versus CL equation above, but K, CD
     C L  a / c  C L(maxL / D )  a / c                                  min and (L/D)max should still be calculated as outlined
        2

                                                                            before neglecting it in the aero database. If not small, a
     And substituting back into the L/D equation yields
                                                                            curve of CL min-D versus Mach is required.
                            a/c
     ( L / D) m ax 
                       2a  b a / c


                                               Hypersonic Educational Initiative
Trends in Subsonic Maximum Lift-to-Drag Ratio




         From Raymer, Daniel P., Aircraft Design: A Conceptual Approach,
         Fourth Edition, AIAA Education Series, 2006

                  Hypersonic Educational Initiative
 Drivers of Transonic and Low-Supersonic
        Aerodynamic Performance
• Transonic wave drag
   – Fineness ratio and area distribution driven

• Inlet drag
   – Body ramps required for high speed inlet efficiency, but . . .
   – Ramps produce spillage drag at transonic and low
     supersonic speeds

• Nozzle drag
   – Large base area required for high speed thrust, but . . .
   – Low nozzle pressure ratios result in aftbody flow
     separation and drag



                 Hypersonic Educational Initiative
    Transonic and Low-Supersonic Wave Drag
• Transonic drag a function of area distribution and fineness ratio

                                     0.24          Mach
                                                  Number
                                                   1.2
        Wave Drag Coefficient, CDw


                                     0.20
                                                   1.1
                                                 1.05                    Note: Wave drag coefficient here is referenced to the body
                                     0.16
                                                1.025                    maximum cross-sectional area and must be re-referenced to
                                                                         vehicle aerodynamic reference area (typically wing planform
                                     0.12          1.0
                                                                         area or vehicle total planform area).

                                     0.08
                                                                                     From Nicolai [5]
                                     0.04

                                       0
                                            0     4        8    12 16 20        24
                                                         Fineness Ratio, B/d
                                        Wave Drag for Parabolic – Type Fuselage



• Flow linear to small perturbations at supersonic speeds, so
  small disturbance theory can be used


                                                      Hypersonic Educational Initiative
 High-Speed Wing Design Issues and Drivers
Wing Issues
• Lift / drag ratio
• Required size
    – Influenced by body and propulsive lift
• Stability and control
• Aerodynamic interaction with propulsion (e.g., inlet & nozzle flow)
• Entry requirements

Wing Design Drivers
• Leading edge sweep
    – Drag and heating effects
• Thickness-to-chord ratio
    – Weight vs. drag
• Axial and vertical placement
    – Stability and control effects



                      Hypersonic Educational Initiative
                           Hypersonic Wave Drag
•   Non-linear flow behavior
•   Disturbances localized (steep Mach and shock waves)
•   Drag a strong function of local surface inclination angle
     – Newtonian Theory example: Cp  sin2 

•   For Mach 3 or 4 and above, can use tangent wedge and tangent cone theory,
    or Newtonian theory for non-wedge/non-cone component geometries
     – For wedge- or cone-shaped surfaces, pressure closely approximated by that
       acting on wedge or cone, respectively, of same total surface angle
          • Total angle is the surface angle in vehicle reference system + angle of attack
     – Newtonian: Cp = 2 sin2 , or (Cp)normal shock stagnation x sin2  (Modified Newtonian),
       where  is the total surface angle
          • Analytically or numerically integrate over component surface
     – Resolve component pressure forces into flight and lift (orthogonal to flight)
       directions, and then sum them to produce total vehicle values

•   Beware of low aspect ratio surfaces: 1-D pressure methods may be
    inaccurate due to dominant 3-D pressure relief effects



                             Hypersonic Educational Initiative
       Trends in Hypersonic Max Lift-to-Drag Ratio

Lift-to-drag ratio (L/D) is a
primary measure of
aerodynamic efficiency

    • Lift generated must
    equal vehicle weight for
    balanced flight                                                Waverider L/D Potential

    • Desire minimum drag
    for lift generated (less
    fuel used, smaller
    vehicle, lower cost)
                                                                      Classical L/D limit




                               Hypersonic Educational Initiative
    Laminar and Turbulent Friction Drag Estimation
•   Use flat plate theoretical formulas with empirical reference-temperature corrections
    for high speeds
                        Laminar                           Turbulent




                           Hypersonic Educational Initiative
          Hypersonic Boundary Layer Transition
        • Boundary layer transition has first order impact on:
            - Aerodynamic drag and control authority
            - Engine performance and operability
            - Thermal protection requirements
                                                                                 Inside Scramjet
            - Structural concepts and weight                                     • Shock-BL Interaction
                                                                                 • Acoustics
• Bluntness                                       •   Curvature                  • Fuel Injection
• Transpiration                                   •   Relaminarization           • Separation
  Cooling                                         •   Roughness
                                                  •   M, Re, 
   • M, Re,                                                         • Bluntness
   • Wall Temperature                                                • Attachment Line Flow
   • Lateral Curvature                                               • Upstream Contamination From Body
   • Nose Bluntness /
     Entropy Swallowing
   • Pressure Gradient                                                               • Tail Deflection
   • Roughness                                                                       • Shock-BL Interaction
                  •   M, Re,                                                        • Roughness
                  •   Wall Temperature
                  •   Lateral Curvature
                  •   Longitudinal Curvature (Gortler)   •   Nonequilibrium            •   Nonequilibrium
                  •   Pressure Gradient                  •   Free Shear Layers         •   Relaminarization
                  •   Roughness                          •   Acoustics                 •   Acoustics
                  •   Shock-BL Interaction               •   Pressure Gradient         •   Film Cooling

            • Many Factors Influence Boundary Layer Transition

                               Hypersonic Educational Initiative
                  Boundary Layer Transition
• Transition from laminar to turbulent flow is driven by many physical
  phenomena
   – First Tollmein – Schlichting mode dominates for adiabatic walls and low hypersonic speeds
     (Mach  7)
   – 2-D second mode dominates for cold walls at hypersonic speeds
                   Re  e Ve 
                                150  300 typical
                   Me    e Me
                   eN stability theory works well for this transition mode (N  10 typical)
   – Cross flow
                              ewmax
                   ReCF =             = 175 – 300 typical
                                 e

                    where wmax = maximum cross flow velocity
                               = boundary layer thickness
   – Attachment line (e.g., leading edges)
                                w 
                   ReAL = AL AL = 100 typical
                                 AL

                   where wAL = spanwise velocity at attachment line
                              = momentum thickness



                          Hypersonic Educational Initiative
    Boundary Layer Transition (Continued)
     – Gortler instability (concave surfaces)

                             
                  G tr  Re     6  10 typical
                            Rc
                      where Rc = radius of curvature of boundary layer streamline
     – Surface roughness
                                    u
                      wukk         y
                                         w
                 Rek =     =                k2 < 25  smooth wall
                        k           w

     – Nose bluntness (entropy layer)

            Bluntness and resulting entropy layer can delay transition if it occurs
            before boundary layer swallows entropy layer

•   Boundary layer transition impacts vehicle drag, heat transfer (and cooling
    requirements), inlet mass capture, inlet compression efficiency, and shear
    layer mixing

     – Transition uncertainty is a key issue for hypersonic air-breathing vehicles




                         Hypersonic Educational Initiative
    Parasite Drag Trend With Mach Number




Fair between Mach 1.2 wave drag + friction and Mach 3 or 4 wave drag + friction




               From Raymer, Daniel P., Aircraft Design: A Conceptual Approach,
               Fourth Edition, AIAA Education Series, 2006

                           Hypersonic Educational Initiative
 Empirical Method For Trending Inviscid CD0
From Hypersonic Speeds to Transonic Speeds
•   Wave drag estimation based on trending drag predictions at Mach 3
    backward with Mach number




                     Hypersonic Educational Initiative

				
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