Comprehensive notes on concentrated vortex flows: sharp-edge and smooth-surface separation, pylon/nacelle vortices, and supersonic transport concepts

2.2.2.4 Supersonic transports

  • Concept: Supersonic transports like Concorde used a thin ogee wing to achieve efficient supersonic cruise and generate high lift from separation-induced leading-edge vortices (LEV) during takeoff/landing.
    • The LEV-based high lift reduces or eliminates the need for mechanical high-lift systems.
  • Operational Considerations:
    • Supersonic operation is restricted to over-sea conditions due to sonic boom concerns.
    • NASA's research program developed a low-sonic-boom concept (e.g., X-59 demonstrator) to enable potential over-land supersonic flight.
  • Design Implications:
    • The ogee wing balances thin-wing supersonic performance with effective leading-edge vortex generation for lift at takeoff/landing.
    • Leading-edge vortices persist and influence overall configuration lift and drag during these regimes.

2.2.3 Summary comments

  • Concentrated vortex flows are exploited to improve aerodynamic performance in both military and civil aircraft.
  • Hierarchical Perspective (from configuration down):
    • Configuration system level: Aerodynamic performance metrics are defined for the entire airframe.
    • Subsystem level: Lifting-surface subsystems (e.g., vortex-lift strake components) contribute to concentrated vortex flows for lift or flow-control benefits.
    • Component level: Subcomponents (e.g., Vortex Generators - VGs) generate concentrated vortex flows within the boundary layer for lift or flow-control effects.
    • Subcomponent level: Vortices interact with boundary layers on a boundary-layer-scale for flow-control.
  • Practical Implications:
    • Vortex persistence and interactions are used to mitigate separation, enhance lift, and influence takeoff/landing performance.
    • Devices like Pylon vortices, nacelle strakes, VGs, and micro-VGs (µVGs) manage separated flow and exploit vortex effects.
  • Example Applications:
    • VGs can relieve buffet and pitch-up on high-speed configurations.
    • µVGs can improve lift by reducing flap separation.

2.3 Elemental flow physics of concentrated vortex flows

  • Objective: Understand fundamental flow-physics components of concentrated vortex flows and how these phenomena manifest in various configurations.
  • Structure:
    • 2.3.1 Flow physics components (elemental components)
    • 2.3.2 Flow-physics manifestations (how components appear in practice)

2.3.1. Flow physics components

  • Focus: Review fundamental flow physics components to understand how vortex flows arise and interact with airframe geometry.
  • Key Concepts:
    • Sharp-edge separation: Baseline for concentrated vortex formation on slender delta wings.
    • Secondary and inner vortices: Arise when smooth-surface separation occurs (blunt-leading-edge cases).
    • Leading-edge vortex (LEV) interaction: How the LEV interacts with the trailing-edge wake and its implications for lift and stability.
2.3.1.1. Sharp-edge separation
  • Baseline: On sharp-edged, highly swept delta wings, flow separates at the leading edge, forming a highly swept free shear layer (vortex sheet).
    • The vortex sheet rolls up to form the primary leading-edge vortex (LEV).
    • The LEV induces reattached flow on the wing upper surface, providing lift via high-speed spanwise flow beneath the vortex.
  • LEV Structure and Core Dynamics:
    • The vortex sheet thickens and can support sub-scale Kelvin-Helmholtz instabilities, creating smaller vortical substructures.
    • The LEV core has two regions:
    • Outer region: Inviscid, rotational flow, governed by Euler equations.
    • Inner region: Viscous subcore, where viscous effects dominate, described by Navier-Stokes equations.
    • The boundary between these regions depends on Reynolds number.
  • Velocity Profiles: Outer core velocities are similar to freestream; axial velocity in the inner core can approach about three times the freestream value.
  • Compressibility and Scale Effects:
    • Compressible effects are relevant within the LEV core at higher Mach numbers.
    • The viscous subcore size decreases with increasing Reynolds number, affecting how close to the axis viscosity removes the singularity.
2.3.1.2. Smooth-surface separation
  • Key Differences: Unlike sharp-edged wings, smooth-surface separation involves:
    • A region of incipient leading-edge separation upstream of the primary vortex.
    • A new inner vortex forming from the primary vortex origin.
    • A persistent region of attached flow from a blunt leading edge, altering overall vortex structure.
  • Challenges: Smooth-surface vortical separation is a major modeling challenge due to simultaneous and interacting flow-physics mechanisms.

2.2.2.2. Pylon vortices and vortilons

  • Pylon Vortices: For swept wings, high-speed flow induces boundary-layer separation over the wing upper surface, forming a longitudinal vortex trailing from the pylon-wing juncture.
    • This vortex reduces spanwise flow, mitigates stall progression, and delays pitch-up, improving stall characteristics.
    • At cruise, the pylon vortex is absent.
  • Vortilons: Truncated pylons that generate a pylon vortex for separation management without an actual nacelle, used to address wing stall and provide lift benefits.

2.2.2.3. Nacelle strakes

  • Purpose: Aerodynamic surfaces that generate concentrated vortices to improve flight characteristics, either by direct vortex-lift effects or by influencing the surrounding flow.
  • Distinction: Strakes are larger and interact more directly with the local inviscid flow compared to smaller vortex generators.
  • Practical Implications: Strakes maintain lift during high-angle-of-attack, high-lift situations on transport aircraft with large engines.

2.2.2.4. Nacelle strake vortices persistence

  • Concept: Vortices generated by nacelle strakes persist over the wing, preserving lift and mitigating stall during takeoff and landing where local separation would reduce lift.

2.3. Flow physics in context

  • Core Mathematical Descriptions:
    • Outer inviscid core: Governed by the Euler equations:
      ρ(dudt)=−∇p+body forces\rho \left(\frac{\text{d} \mathbf{u}}{\text{d}t}\right) = -\nabla p + \text{body forces}
      ∇×u≠0\nabla \times \mathbf{u} \neq 0
      ∇×u finite\nabla \times \mathbf{u} \text{ finite}
      ∇×u nonzero in core\nabla \times \mathbf{u} \text{ nonzero in core}
    • Inner viscous subcore: Described by the Navier–Stokes equations:
      ρ(dudt)=−∇p+∇(τ)+body forces, with τ=∇u+(∇u)T\rho \left(\frac{\text{d} \mathbf{u}}{\text{d}t}\right) = -\nabla p + \nabla (\mathbf{\tau}) + \text{body forces}, \text{ with } \mathbf{\tau}=\nabla \mathbf{u} + (\nabla \mathbf{u})^T
    • Reynolds number definition: Re=ρULμ (or Re=ρULν)Re =\frac{\rho U L}{\mu} \text{ (or } Re =\frac{\rho U L}{\nu}\text{)}
    • Inner-law scaling example:
      V<em>θ (circumferential)∼O(1)×V</em>inf, V<em>z (axial)∼3×V</em>infV<em>\theta \text{ (circumferential)} \sim O(1) \times V</em>\text{inf}, \ V<em>z \text{ (axial)} \sim 3 \times V</em>\text{inf}
  • Practical Implications for Design and Analysis:
    • LEV structure and its subregions influence lift, stall, and control on