The GATE Grind

GATE 2023 AE – Question 46

Aerodynamics · Airfoils and wings: coefficients, Kutta-Joukowski theorem, thin airfoil theory, finite wing theory, critical and drag divergence Mach numbers · 2 marks · Multiple select

For an airfoil, which critical and drag-divergence Mach-number relations are correct?

  1. $M_{cr}<M_{dd}$
  2. $M_{cr}<1$
  3. $M_{dd}<1$
  4. $M_{cr}>1$

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Correct answer: (A) $M_{cr}<M_{dd}$; (B) $M_{cr}<1$; (C) $M_{dd}<1$

Explanation

Definitions:
- **Critical Mach number $M_{cr}$:** the free-stream Mach number at which the local Mach number first reaches 1 somewhere on the airfoil.
- **Drag-divergence Mach number $M_{dd}$:** the free-stream Mach number at which the drag starts to rise sharply because of shock waves.

At $M_{cr}$ the free stream is still subsonic, since the local flow over the airfoil is faster than the free stream. So:
- **B. $M_{cr}<1$.** ✓
- **D. $M_{cr}>1$.** ✗
- **A. $M_{cr}<M_{dd}$.** The shock waves must first appear (at $M_{cr}$) and then strengthen until the drag rises sharply, so drag divergence occurs after the critical Mach number. ✓
- **C. $M_{dd}<1$.** For conventional airfoils the drag rise happens at a subsonic free-stream Mach number (typically 0.8 to 0.95). ✓

Answer **A, B and C**.