Tema1, Apuntes de Ingeniería Aeroespacial

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Flight Principles

Aerospace Science & Technology

F. Mellibovsky

Escola d’Enginyeria de Telecomunicaci´o i Aeroespacial de Castelldefels Universitat Polit`ecnica de Catalunya

February 22, 2011

Summary

Let’s get Airborne Environmental Model The Earth The Atmosphere

Mechanical Model Reference Frames Equations: Newton Laws for a Rigid Body

Aerodynamical Model Fluid Dynamics Basics Aerofoil Aerodynamic Forces Wing Aerodynamic Forces Aircraft Aerodynamic Forces Propulsive Model

Simple Flight Equilibria

The Aircraft (Parts)

The Aircraft (Model)

Hypothesis: I (^) Constant mass I (^) Rigid body I (^) Reflection-symmetric

The Wing

1 winglet 2,3 ailerons (outboard, inboard) 4 flap deployment system 5,6 slats (inboard, outboard) 7,8 flaps (inboard, outboard) 9,10 spoilers (outboard, inboard)

The Aerofoil

Parts: I (^) Leading Edge I (^) Trailing Edge I (^) Intrados / Lower Surface I (^) Extrados / Upper Surface Naming: I (^) l: Chord I (^) t: Thickness I (^) c: Camber I (^) α: Angle of attack

The Earth

Hypothesis: (M = 2, h = 20km) I (^) Steady earth: (0.8%)

acoriolis agravity

2Ωe V g

I (^) Flat earth: (0.6%)

acentripetal agravity

V 2

Re g

I (^) Constant gravity: (0.6%)

g 0 − gh g 0

(1 + h/Re )^2

Air

Composition of dry air (volume fraction):

I (^78) .1% Nitrogen (N 2 ) I (^20) .9% Oxigen (O 2 ) I (^0) .9% Argon (Ar) I (^0) .1% Other gases

Water vapor (H 2 O): 0.4% (1-4% at sea level)

Properties (sea level values ISA): I (^) p: Pressure (p 0 = 101325Pa) I (^) T : Temperature (T 0 = 288. 15 K ) I (^) ρ: Density (ρ 0 = 1. 225 kg /m^3 ) I (^) μ: Dynamic viscosity (μ 0 = 1. 7810 −^5 Pa · s) I (^) R = R/M: Air constant (287. 14 J/(Kg K )) I (^) Cp , Cv : specific heat capacities (J/(Kg K )) Derived Properties: I (^) γ = Cp /Cv : Adiabatic index (1.4) I (^) a =

γRT : Speed of sound (m/s) I (^) ν = μ/ρ: Kinematic viscosity (m^2 /s) Flow parameters: I (^) M = V /a: Mach number I (^) Re = VL/ν: Reynolds number

Outline

Let’s get Airborne Environmental Model The Earth The Atmosphere

Mechanical Model Reference Frames Equations: Newton Laws for a Rigid Body

Aerodynamical Model Fluid Dynamics Basics Aerofoil Aerodynamic Forces Wing Aerodynamic Forces Aircraft Aerodynamic Forces Propulsive Model

Simple Flight Equilibria

Body Axes

Equations (Rigid Body Dynamics)

6 second-order equations: I (^) Linear Momentum Equation

m

d^2 r~G dt^2

F~ext = ~F + T~ + W~

I (^) Angular Momentum Equation

d dt

(IG ~ω) =

M~G ,ext = M~F + M~T

or 12 first-order equations: I (^) Horizontal Homogeneity and Isotropy: Position (xG , yG ) and rhumb (ψ) without influence on forces −→ 9 equations I (^) Decoupling Hypothesis: 5 Longitudinal, 4 lateral.

Outline

Let’s get Airborne Environmental Model The Earth The Atmosphere

Mechanical Model Reference Frames Equations: Newton Laws for a Rigid Body

Aerodynamical Model Fluid Dynamics Basics Aerofoil Aerodynamic Forces Wing Aerodynamic Forces Aircraft Aerodynamic Forces Propulsive Model

Simple Flight Equilibria

General Equations & Simplifications

Useful simplifications in aerodynamics: I (^) Inviscid / viscous regions decoupling: I (^) Inviscid flow −→ Euler Equations (most of the domain) Re  I (^) Boundary Layer Equations (close to solid obstacles) I (^) Low-pass filtering + turbulence modelling I (^) ideal gas (simple state equations) I (^) Incompressible flow (irrotational or potential flow) M  I (^) Stationary flow (permanent regime) I (^) Geometric simplifications (2D flow, axisymmetric flow...) Flow regimes for gases: I (^) Low Subsonic / Incompressible: M. 0. 3 I (^) Subsonic Compressible: 0. 3. M. 0. 75 I (^) Transonic: 0. 75. M < 1. 2 I (^) Supersonic: M > 1. 2 I (^) Hypersonic: M & 5

Mass & Momentum Conservation

Mass Conservation:

I (^) stationary flow ∑ i ρi^ (^ V~i · ~ni )Ai = 0 I (^) stream tube ρ 2 V 2 A 2 − ρ 1 V 1 A 1 = 0 I (^) incompressible flow V 2 A 2 − V 1 A 1 = 0

Momentum Conservation: I (^) stationary flow ∑ i

pi n~i + ρi V~i ( V~i · ~ni )

Ai = ~Fext I (^) stream tube∑ i

pi + ρi V (^) i^2

Ai~ni = ~Fext