An introduction to Aerodynamics PDF
Preview An introduction to Aerodynamics
Gestione dei sistemi aerospaziali per la difesa Universit`a di Napoli Federico II - Accademia Aeronautica di Pozzuoli Aerodynamics R.Tognaccini An introduction to Aerodynamics Introduction Hydrostatics Fundamental principles Renato Tognaccini1 Incompressible inviscidflow Effectsof DipartimentodiIngegneriaIndustriale, viscosity Universit`adiNapoliFedericoII Effectsof compressibility Aircraft lift-dragpolar [email protected] Some definitions Aerodynamics R.Tognaccini Fluid a substance without its own shape; Introduction characterized by its own volume (liquid) or by Hydrostatics the volume of the container (gas). Fundamental principles Continuum each part of the fluid, whatever small, contains Incompressible a very large (infinite) number of molecules. inviscidflow Fluid particle an infinitely small volume in the (macroscopic) Effectsof viscosity scale of our interest, but sufficiently large in the Effectsof (microscopic) length scale of molecules in order compressibility to contain an infinite number of molecules. Aircraft lift-dragpolar Aerodynamics branch of Fluid Mechanics concentrating on the interaction between a moving body and the fluid in which it is immersed. The aerodynamic forces Aerodynamics O(x,y,z) inertial reference system fixed to the aircraft. R.Tognaccini V aircraft speed at flight altitude h characterized by pressure Introduction ∞ p and density ρ . ∞ ∞ Hydrostatics Fundamental principles Dynamic equilibrium Incompressible inviscidflow Effectsof L = W T = D (1) viscosity Effectsof compressibility L lift ⊥V Aircraft ∞ lift-dragpolar D drag (cid:107) V ∞ W aircraft weighta T thrust a Gisthecenterofgravity The aerodynamic force coefficients Aerodynamics R.Tognaccini 12ρ∞V∞2 S reference force Introduction S reference surface (usually wing surface Sw) Hydrostatics Fundamental Lift and drag coefficients principles Incompressible inviscidflow L D C = C = (2) Eviffsceocstistyof L 12ρ∞V∞2S D 12ρ∞V∞2S Effectsof compressibility Aircraft Aerodynamic efficiency lift-dragpolar L C L E = = (3) D C D Practical applications Aerodynamics R.Tognaccini Problem n. 1 Introduction Compute lift coefficient of an aircraft in uniform horizontal Hydrostatics flight: 1 W Fundamental principles CL = 1ρ V2 S (4) Incompressible 2 ∞ ∞ inviscidflow Effectsof viscosity Problem n. 2 Effectsof compressibility Compute stall speed of an aircraft in uniform horizontal flight: Aircraft lift-dragpolar (cid:115) (cid:114) (cid:115) 1 W 2 V = (5) s C S ρ Lmax ∞ Fundamental flow parameters Mach number Aerodynamics R.Tognaccini Mach number definition Introduction V Hydrostatics M = (6) Fundamental a principles V: fluid particle velocity, a: local sound speed Incompressible inviscidflow Effectsof A flow with constant density everywhere is called viscosity incompressible. Effectsof compressibility Liquids are incompressible. Aircraft lift-dragpolar In an incompressible flow M = 0 everywhere. In some circumstances compressible fluids (gas) behave as incompressible (liquid): M → 0. Fundamental flow parameters Reynolds number 1/2 Aerodynamics Reynolds number definition R.Tognaccini Introduction ρVL Hydrostatics Re = (7) µ Fundamental principles L: reference length, µ: dynamic viscosity (Kg) Incompressible ms inviscidflow Effectsof viscosity Newtonian fluid Effectsof compressibility ∂V Aircraft dF = µ dA (8) lift-dragpolar ∂z Friction proportional to velocity gradient in the flow. Afluidflowingonasolidplate. Fundamental flow parameters Reynolds number 2/2 Aerodynamics The Reynolds number compares dynamic forces R.Tognaccini (associated with momentum of fluid particles) against Introduction friction forces (associated with momentum of molecules). Hydrostatics A flow in which µ = 0 is named inviscid or not dissipative. Fundamental principles In an inviscid flow Re = ∞ and friction can be neglected. Incompressible inviscidflow kinematic viscosity: Effectsof viscosity Effectsof µ (cid:18)m2(cid:19) compressibility ν = (9) ρ s Aircraft lift-dragpolar For air in standard conditions: ν ≈ 10−5m2. s In Aeronautics usually Re (cid:29) 1: in many aspects (but not all) the flow behaves as inviscid. Flow regimes Aerodynamics Based on Mach number: R.Tognaccini M = 0 (everywhere) incompressible flow Introduction M (cid:28) 1 (everywhere) iposonic flow Hydrostatics Fundamental M < 1 (everywhere) subsonic flow principles Incompressible M < 1 and M > 1 transonic flow inviscidflow M > 1 (everywhere) supersonic flow Effectsof viscosity M (cid:29) 1 hypersonic flow Effectsof compressibility Aircraft lift-dragpolar Based on Reynolds number: Re → 0 Stokes (or creeping) flow Re → ∞ ideal flow Critical Mach numbers Aerodynamics R.Tognaccini M(cid:48) lower critical Mach number: freestream Mach ∞,cr Introduction number producing at least one point in which M = 1 Hydrostatics whereas elsewhere M < 1 Fundamental M(cid:48)(cid:48) upper critical Mach number: freestream Mach principles ∞,cr number producing at least one point in which M = 1 Incompressible inviscidflow whereas elsewhere M > 1 Effectsof viscosity Effectsof compressibility Aircraft lift-dragpolar M∞ < M∞(cid:48) ,cr subsonic regime M(cid:48) < M < M(cid:48)(cid:48) transonic regime ∞,cr ∞ ∞,cr M > M(cid:48)(cid:48) supersonic regime ∞ ∞,cr
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