✈️Aerodynamics Unit 9 – High–speed aerodynamics

Key Concepts and Principles

• High-speed aerodynamics deals with fluid flow at speeds approaching or exceeding the speed of sound (Mach 1)
• Compressibility effects become significant at high Mach numbers, leading to changes in flow behavior and aerodynamic forces
  • Density variations can no longer be neglected and the flow is treated as compressible
  • The relationship between pressure, density, and temperature is governed by the ideal gas law
• The Mach number ($M = \frac{v}{a}$) is a crucial parameter in high-speed aerodynamics, representing the ratio of the flow velocity to the local speed of sound
• As Mach number increases, the flow undergoes a transition from subsonic to transonic, supersonic, and hypersonic regimes, each with distinct characteristics
• Shock waves form when the flow encounters an obstacle or experiences a sudden change in pressure, resulting in a nearly instantaneous change in flow properties
• Expansion fans occur when the flow expands around a corner or a sharp edge, causing a gradual change in flow properties
• The Prandtl-Glauert transformation relates subsonic and supersonic flow, allowing for the analysis of compressible flow using incompressible flow methods

Compressibility Effects

• Compressibility effects arise due to the finite speed of sound in a fluid, causing density variations in high-speed flows
• As Mach number increases, the flow becomes increasingly sensitive to pressure changes, leading to the formation of shock waves and expansion fans
• The Prandtl-Glauert compressibility correction factor ($\beta = \sqrt{1 - M^2}$) accounts for the effects of compressibility on aerodynamic coefficients
• The critical Mach number ($M_{cr}$) is the freestream Mach number at which the local flow reaches Mach 1, marking the onset of transonic flow
• Compressibility effects can lead to significant changes in lift, drag, and pitching moment coefficients compared to incompressible flow
• The drag divergence Mach number ($M_{dd}$) is the freestream Mach number at which the drag coefficient begins to increase rapidly due to the formation of shock waves
• Compressibility effects can cause flow separation, buffeting, and control surface effectiveness issues at high Mach numbers

Shock Waves and Expansion Fans

• Shock waves are thin regions of nearly discontinuous changes in flow properties (pressure, density, temperature, and velocity) that occur when a supersonic flow encounters an obstacle or experiences a sudden compression
• Normal shock waves are perpendicular to the flow direction and cause a sudden deceleration of the flow from supersonic to subsonic speeds
  • The Rankine-Hugoniot equations describe the relationships between flow properties across a normal shock wave
• Oblique shock waves form when a supersonic flow encounters a sharp corner or wedge at an angle, causing a sudden deflection of the flow and a change in properties
  • The oblique shock angle and the downstream flow properties depend on the freestream Mach number and the deflection angle
• Bow shocks occur ahead of blunt bodies in supersonic flow, forming a detached curved shock wave that envelops the body
• Expansion fans are regions of gradual changes in flow properties that occur when a supersonic flow expands around a corner or a sharp edge
  • Prandtl-Meyer expansion waves are isentropic and result in an increase in Mach number and a decrease in pressure and density
• Shock-expansion theory combines the analysis of oblique shock waves and Prandtl-Meyer expansions to predict the flow properties and aerodynamic forces on supersonic airfoils and wings

Supersonic Airfoil Theory

• Supersonic airfoil theory deals with the design and analysis of airfoils operating at Mach numbers greater than 1
• The Ackeret theory provides a linearized approach to calculate the lift and pressure distribution on a thin, uncambered airfoil in supersonic flow
  • The lift coefficient is proportional to the angle of attack and inversely proportional to the Mach number
• The Busemann theory extends the analysis to include the effects of airfoil thickness and camber in supersonic flow
  • The airfoil is represented by a distribution of sources and sinks, and the flow properties are obtained using the method of characteristics
• The shock-expansion theory is a more accurate method that accounts for the presence of shock waves and expansion fans on the airfoil surface
  • The airfoil is divided into regions of uniform flow separated by oblique shock waves and Prandtl-Meyer expansions
• Supersonic airfoils typically have a sharp leading edge to minimize the strength of the bow shock and reduce wave drag
• The biconvex and double-wedge airfoils are common supersonic airfoil shapes that provide a balance between aerodynamic performance and structural integrity
• Supersonic airfoils often employ a blunt trailing edge to reduce the intensity of the rear shock wave and improve the pressure recovery

High-Speed Aircraft Design Considerations

• High-speed aircraft design involves optimizing the aerodynamic, structural, and propulsion systems to achieve efficient and stable flight at supersonic and hypersonic Mach numbers
• The area rule states that the cross-sectional area distribution of an aircraft should be smooth and continuous to minimize wave drag at transonic and supersonic speeds
  • The Sears-Haack body represents the ideal cross-sectional area distribution for minimum wave drag
• Swept wings are commonly used in high-speed aircraft to delay the onset of compressibility effects and reduce wave drag
  • The critical Mach number increases with wing sweep, allowing for higher speeds before the formation of strong shock waves
• Thin airfoils with sharp leading edges are preferred for supersonic flight to minimize wave drag and improve aerodynamic efficiency
• Supersonic inlets are designed to decelerate the incoming flow to subsonic speeds before entering the engine, while minimizing total pressure loss and flow distortion
  • Cone-shaped spike inlets and ramp inlets are common types of supersonic inlets
• Nozzle design is critical for efficient thrust generation in high-speed aircraft, with convergent-divergent nozzles being the most suitable for supersonic exhaust flows
• Thermal management becomes increasingly important at high Mach numbers due to aerodynamic heating caused by friction and compression effects
  • Ablative materials, active cooling systems, and heat-resistant alloys are used to protect the aircraft structure from extreme temperatures

Experimental Methods and Wind Tunnels

• Experimental methods and wind tunnel testing play a crucial role in validating theoretical predictions and assessing the performance of high-speed aircraft and components
• Supersonic wind tunnels are designed to generate high-quality, uniform flow at Mach numbers greater than 1
  • Converging-diverging nozzles are used to accelerate the flow to supersonic speeds, and the test section size is limited by the available power and flow quality requirements
• Transonic wind tunnels are used to study the flow behavior around Mach 1, often employing perforated or slotted walls to minimize blockage effects and wall interference
• Hypersonic wind tunnels achieve Mach numbers greater than 5 and are used to investigate the flow phenomena and aerodynamic heating effects relevant to hypersonic flight and atmospheric reentry
• Shock tubes and shock tunnels generate short-duration, high-enthalpy flows for studying high-temperature gas dynamics and aerothermodynamics
• Schlieren and shadowgraph imaging techniques are used to visualize density gradients in compressible flows, enabling the observation of shock waves, expansion fans, and boundary layers
• Pressure-sensitive paint (PSP) and temperature-sensitive paint (TSP) are optical measurement techniques that provide high-resolution surface pressure and temperature distributions in wind tunnel tests
• Force and moment measurements using strain gauge balances, pressure measurements using pressure transducers, and flow field measurements using pitot probes and hot-wire anemometers are common in high-speed wind tunnel testing

Computational Fluid Dynamics in High-Speed Flow

• Computational Fluid Dynamics (CFD) has become an essential tool for analyzing and predicting high-speed flow phenomena and aerodynamic performance
• The governing equations for compressible flow, such as the Euler equations and the Navier-Stokes equations, are solved numerically using finite difference, finite volume, or finite element methods
• Shock-capturing schemes, such as the Godunov method and the Roe scheme, are used to accurately resolve shock waves and discontinuities in the flow field
• Turbulence modeling is crucial for simulating high-speed turbulent flows, with models ranging from Reynolds-Averaged Navier-Stokes (RANS) equations to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS)
• Adaptive mesh refinement techniques are employed to efficiently capture flow features of interest, such as shock waves and boundary layers, while minimizing computational cost
• High-performance computing (HPC) and parallel processing are essential for handling the large computational demands of high-speed flow simulations
• CFD simulations are used in conjunction with experimental data for validation and verification purposes, ensuring the accuracy and reliability of numerical predictions
• Aerodynamic shape optimization using CFD has become increasingly popular in high-speed aircraft design, allowing for the exploration of novel configurations and the improvement of existing designs

Real-World Applications and Case Studies

• High-speed aerodynamics has numerous real-world applications, ranging from commercial supersonic flight to military aircraft, missiles, and spacecraft
• The Concorde, a supersonic passenger airliner that operated from 1976 to 2003, is an iconic example of high-speed aircraft design and engineering
  • The Concorde utilized a slender, ogival fuselage, swept delta wings, and variable-geometry engine inlets to achieve efficient supersonic cruise performance
• Modern military fighter aircraft, such as the F-22 Raptor and the F-35 Lightning II, employ advanced high-speed aerodynamic design features for enhanced maneuverability, stealth, and supersonic cruise capability
• Supersonic business jets, such as the proposed Aerion AS2 and the Spike S-512, aim to provide fast and efficient transportation for high-net-worth individuals and corporate executives
• Hypersonic vehicles, including scramjets (supersonic combustion ramjets) and boost-glide vehicles, are being developed for various applications, such as rapid global strike, reconnaissance, and space access
  • The X-43A, an experimental hypersonic aircraft, achieved a record speed of Mach 9.6 using a scramjet engine
• Spacecraft and atmospheric entry vehicles, such as the Space Shuttle and the Orion capsule, experience high-speed flow during ascent and reentry phases
  • The design of thermal protection systems and the prediction of aerodynamic heating are critical aspects of spacecraft design and mission planning
• Rockets and missiles, including intercontinental ballistic missiles (ICBMs) and air-to-air missiles, operate at high Mach numbers and require careful consideration of compressibility effects and aerodynamic stability
• High-speed wind tunnels and CFD simulations have been instrumental in the development and optimization of high-speed vehicles, from the early X-series aircraft to modern supersonic and hypersonic designs