Hypersonic Vehicle Systems Integration Vehicle Aerodynamic Analysis

1
Hypersonic Vehicle Systems IntegrationVehicle
Aerodynamic Analysis

• 12 September, 2007
• Dr. Kevin G. Bowcutt
• Senior Technical Fellow
• Chief Scientist of Hypersonics
• Boeing Phantom Works

2
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)

3
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)

4
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

5
Elements of Subsonic Wing and Body Lift

• Wing / body camber
• Lift system aspect ratio
• Vortex lift
• Ground effects
• Powered and un-powered

6
Linear Contributions to SubsonicWing 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
7
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
c
From Nicolai 5
Linear Part
AoA
From Newsome and Kandil 6
8
Non-linear Vortex Lift on Rectangular and Delta
Wings
0.6
c
b
CL
A I / 5
a
0.4
0.2
Lin. Theory

• Low aspect ratio rectangular wings with stable
  leading edge separation
• Thin Wing
• Thick Wing
• Thin delta wings

0
5
0
10
15
20
25
?
Exp. Flachsbart (1932) Thin Plate Exp. Prandtl -
Betz (1920) Thick Wing
c
b
1.0
CL
A I
a
0.8
? 2
? 2
3/2
CL AR ? ?
(Curve c on plot)
0.6
Lin. Theory
0.4
? 2
? 2
2
CL AR ? ?
(Curve a on plot)
0.2
5
0
10
25
15
20
? - ?o
Overall lift of rectangular wings of small aspect
ratio
20
1.7
? s / ?
Experiments s/? Brown Michael (1954) 0.088
Fink Taylor (1955) 0.18 Peckham (1958) 0.25
Marsden, et al (1958) 0.36
CN / (s / ?)2 2?? / (s / ?) 4.9
s b/2 wing half-span ? wing root-chord
10
? s / ?
2?
0
0.5
1.0
1.5
Normal forces on slender delta wings
From Küchemann 7
9
Angle of Attack Limits for Low Speed Flight
Vortex Contact or Asymmetry
40
30
Vortex Breakdown
Angle of Attack (Deg)
Complete Recovery of Leading Edge Suction
as Normal Force
20
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
10
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

11
Powered Ground Effects Model Details
24.00
75
43.58
112.89
MomentReferenceCenter
Air Sting
37.5
Balance Fairing
12.00
10
14
Ground Height Reference Point
Engine Simulators
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
12
Ground Effects for Variations in Thrust
Coefficient at 12-Degrees Angle of Attack
0.20
CT q ?, psf 0 40 0.2 40 0.4 40
0.6 26 0.8 20
0.15
0.10
Cm
0.05
0.2
0
0.3
0
0.2
-0.2
0.1
CD
-0.4
0
CL
-0.1
-0.6
Approximate Wheel Touchdown Height
Approximate Wheel Touchdown Height
-0.2
-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
  ground effects (i.e., suction) at take-off

Courtesy of Greg Gatlin, NASA Langley
13
Ground Effects for Variations in Angle of Attack
at 0.4 Thrust Coefficient and 40 psf Dynamic
Pressure
0.20
0.15
0.10
Cm
0.05
0
0.3
0.2
0.1
0.1
0
CL
0
-0.1
CD
-0.1
-0.2
-0.2
-0.3
1.0
2.0
3.0
0
-0.3
h / b
1.0
2.0
3.0
0
h / b

• Powered ground effects increase lift at large
  angles of attack and decrease lift at low angles
  of attack

Courtesy of Greg Gatlin, NASA Langley
14
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)

15
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

Note If CL min-D is very small, then it could be
neglected in the quadratic CD versus CL equation
above, but K, CD min and (L/D)max should still be
calculated as outlined before neglecting it in
the aero database. If not small, a curve of CL
min-D versus Mach is required.
16
Trends in Subsonic Maximum Lift-to-Drag Ratio
From Raymer, Daniel P., Aircraft Design A
Conceptual Approach, Fourth Edition, AIAA
Education Series, 2006
17
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

18
Transonic and Low-Supersonic Wave Drag

• Transonic drag a function of area distribution
  and fineness ratio
• Flow linear to small perturbations at supersonic
  speeds, so small disturbance theory can be used

Note Wave drag coefficient here is referenced to
the body maximum cross-sectional area and must be
re-referenced to vehicle aerodynamic reference
area (typically wing planform area or vehicle
total planform area).
From Nicolai 5
19
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

20
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

21
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
• Desire minimum drag for lift generated (less
  fuel used, smaller vehicle, lower cost)

Waverider L/D Potential
Classical L/D limit
22
Laminar and Turbulent Friction Drag Estimation

• Use flat plate theoretical formulas with
  empirical reference-temperature corrections for
  high speeds

Laminar
Turbulent
23
Hypersonic Boundary Layer Transition

• Boundary layer transition has first order impact
  on
• Aerodynamic drag and control authority
• Engine performance and operability
• Thermal protection requirements
• Structural concepts and weight

• Inside Scramjet
• Shock-BL Interaction
• Acoustics
• Fuel Injection
• Separation

• Bluntness
• Transpiration Cooling

• Curvature
• Relaminarization
• Roughness
• M, Re, a

• M, Re, a
• Wall Temperature
• Lateral Curvature
• Nose Bluntness /Entropy Swallowing
• Pressure Gradient
• Roughness

• Bluntness
• Attachment Line Flow
• Upstream Contamination From Body

• Tail Deflection
• Shock-BL Interaction
• Roughness

• M, Re, a
• Wall Temperature
• Lateral Curvature
• Longitudinal Curvature (Gortler)
• Pressure Gradient
• Roughness
• Shock-BL Interaction

• Nonequilibrium
• Relaminarization
• Acoustics
• Film Cooling

• Nonequilibrium
• Free Shear Layers
• Acoustics
• Pressure Gradient

• Many Factors Influence Boundary Layer Transition

24
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
• eN stability theory works well for this
  transition mode (N ? 10 typical)
• Cross flow
• ReCF 175 300 typical
• where wmax maximum
  cross flow velocity
• ? boundary
  layer thickness
• Attachment line (e.g., leading edges)
• Re?AL 100 typical
• where wAL spanwise velocity
  at attachment line
• ? momentum thickness

?ewmax? ?e
?ALwAL? ?AL
25
Boundary Layer Transition (Continued)

• Gortler instability (concave surfaces)
• where Rc radius of curvature of boundary
  layer streamline
• Surface roughness
• 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

?u ?y
?wukk ?k
w
Rek k2 lt 25 ?
smooth wall
?w
26
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
27
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