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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) 2AR CL = 2+ 4 + AR22 (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 inD ) 2 C Dm in KC L m in D 2 KC Lm inD C L KC L 2 2 CD Set a C Dm in KC L m in D 2 b 2 KC Lm inD cK 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 inD , and C Dm in can be obtained from the parabola coefficients CD min K c CL C Lm inD 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 ReAL = 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