High Speed Aero

• At M>0.3, flow becomes compressible
• The critical pressure coefficient and free stream Mach number tells us when sonic flow occurs
• For a supercritical aerofoil:

  • The upper surface is flattened so that the mach number remains constant over a large length
  • Since the shock wave strength on the upper is lower, the boundary layer separation is less severe meaning the critical mach number is higher before drag divergence
  • The drag divergence mach number is higher.
  • The best supercritical aerofoil is shock free, 2nd best is one with weak and far back shock-wave to minimize separation
• p-p_inf = rho_inf v_inf dv , Euler equation, used in linearised aero foil derivation
• Cpu is + ve, Cpl is - ve
• • Crocco's theorem relates entropy to vorticity.
  • Plane shock waves with no intersections have uniform flow fields and therefor no entropy gradients.
  • Flow is irrotational both up and downstream of shock, but not at the shock itself.
  • This is because at the shockwave the intense entropy gradient is associated with an intense generation of vorticity but the vorticity is dissipated at the same rate it generates.
  • For curved shockwaves the whole flow field contains an entropy gradient and therefor downstream flow is rotational.
• • Crocco's theorem proves shockwaves can act as a source of vorticity.
  • Expansion waves are isentropic, so a steady adiabatic flow with expansion waves is irotational.
  • Shockwaves cause intense entropy gradients at the location of the shock, so strong vorticity transport effects are present according to the theorem.
• As M > Mcrit:

  • Small pockets of supersonic flow form.
  • Supersonic flow is terminated by a very weak shock.
• Mcrit < Minf < 1:

  • Supersonic region grows in chordwise and normal direction, terminating shock gets stronger.
  • Delta or Lambda structure form at shock root due to shock boundary layer interaction.
  • Flow behind shock separates, may reattach forming bubble.
  • Supersonic flow and shock will be present on lower surface, not at same positions for asymmetric aerofoil or at incidence.
  • Flow structure alter significantly with small change in M, highly dependent on geometry.
• 1 < Minf < 1.2:

  • Approach flow is now supersonic, shockwaves dominate flow at leading and trailing edge.
  • Low supersonic value means leading edge shock is detached and forms bow shock,
  • Bow shock creates zone of locally subsonic flow at leading edge.
  • Sonic flow at more inclined regions of bow shock and over surface where high acceleration.
  • Trailing edge shocks turn flow parallel.
  • As M rises subsonic region decreases, bow shock attaches, flow is supersonic.
• T ∇ s = ∇ ho - V x (∇ x V)+dV/dt
• The assumptions in the analysis of an oblique shockwave are:

  • Viscous effects are negligible
  • The flow is steady and adiabatic
  • The flow is not isentropic
• When alpha = 0, the s-n and x-y axes are aligned