Aerodynamics Lecture Notes

Introduction

• Continuation of Chapter One: Principles of Aerodynamics
• Focus on definition and introductory thoughts on aerodynamics
• Previous discussion on flow similarity
• Flow similarity requires: similar bodies, same Reynolds number, same Mach number, same angle of attack

Example Problem (Based on Anderson's Book Example 1.5)

• Flight Parameter: Airplane flight at 885 km/hr, altitude 12 km
• Known Data: Density, temperature, and pressure at this altitude (from standard atmosphere table)
• Objective: Test a scale model in a wind tunnel (scale 1:50)
  • Fixed temperature inside the wind tunnel: 240 K
  • Calculate Reynolds number and Mach number for both actual flight and wind tunnel test to maintain similarity

Assumptions and Definitions

• Viscosity proportional to the square root of temperature
• Mach Number: Velocity / Speed of sound
• Reynolds Number: [ \text{Re} = \frac{\rho V L}{\mu} ] where (\rho) is density, (V) is velocity, (L) is characteristic length, and (\mu) is dynamic viscosity

Calculations

• Mach Number Calculation: [ M = \frac{V}{a} ] [ V_1 = V_\infty \sqrt{\frac{T_1}{T_\infty}}] ( V_1 \approx 932 ) m/s (velocity inside the wind tunnel)
• Reynolds Number Calculation:
  • Proportional Relation: [ \text{Re} \propto \frac{V \rho L}{\sqrt{T}} ]
  • Density Calculation for Wind Tunnel: [ \rho_1 = \rho_\infty \frac{C_\infty}{C_1} \sqrt{\frac{T_1}{T_\infty}} ] ( \rho_1 \approx 16.6 ) kg/m³

Practical Implications

• High velocity and high density required in wind tunnel to maintain test conditions
• Wind tunnel must allow control over both velocity and density
• Variable density wind tunnels are complex and expensive
• Alternative testing approaches: maintain same Mach or Reynolds number separately

Theory of Aerodynamics

• Buckingham π Theorem: Aerodynamic coefficients function of Reynolds, Mach, and angle of attack
• Lift & Drag Coefficients:
  • Lift Coefficient varies linearly with angle of attack up to a maximum point (related to stall)
  • Drag Coefficient minimum at low angles of attack, increases with angle
• Aerodynamic Coefficients: Lift force divided by dynamic pressure and reference area
• Stall Velocity: Minimum flight velocity corresponding to maximum angle of attack
• Lift to Drag Ratio (L/D): Important criteria for aerodynamic efficiency [ \frac{L}{D} = \frac{C_L}{C_D} ]

Example Calculations from Anderson's Textbook

Example 1.6

• Flight Data: Altitude, velocity, weight, density, drag coefficient, reference area
• Lift Coefficient: [ C_L = \frac{L}{q_\infty S} ] ( C_L \approx 0.21 )
• Lift to Drag Ratio: [ \frac{L}{D} \approx 14 ]

Takeoff Condition Calculation

• Maximum lift coefficient: [ C_{L_{ ext{max}}} \approx 1.82 ]

Types of Flows

• Free Molecular vs. Continuum Flow
• Inviscid vs. Viscous Flow
• Compressible vs. Incompressible Flow
• Mach Number Regimes:
  • Subsonic
  • Transonic
  • Supersonic
  • Hypersonic

Detailed Discussion of Flow Types

• Transonic Flow: Contains both subsonic and supersonic regions
• Supersonic Flow: Shock waves and expansion waves
• Hypersonic Flow: Comprehensive models involving chemistry and ionization

Boundary Layers

• Definition: Velocity changes near the body due to viscosity
• Types: Laminar and Turbulent
• Significance: Important in determining aerodynamic performance
• Boundary Layer Thickness: Point where velocity change ceases
  • Related to velocity profile gradient
• Thermal Boundary Layer: Changes in temperature near the body

Upcoming Topics

• Next Lecture: Magnitudes and variations of aerodynamic coefficients
• Work 1: Practical calculation and presentation of aerodynamic quantities

Conclusion

• No class tomorrow; continue next week
• Questions and discussions are encouraged