By K Attenborough; V I Tokarev; Oleksandr Zaporozhets
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Extra info for Aircraft noise propagation, exposure & reduction : assessment , prediciton and control
16 Consequently, aviation noise reduction through operating procedures depends on communication between airlines, airports and the Civil Aviation Authority. The abatement of aircraft noise involves limiting the noise at the source, noise control along the sound transmission path, low noise takeoff and approach ﬂight procedures, optimal distribution of aircraft between the arrival and departure routes and land-use planning. Methods of noise abatement can be realized at all stages of the ‘life cycle’ of aircraft, from designing to aircraft phase-out.
1), one obtains ρ0 ∂ vi ∂ p + = 0. 19) over time yields vi = − 1 ∂ ρ0 ∂ x i p dt . 20) So, the acoustical ﬁeld is irrotational and can be described in terms of a velocity potential ϕ , given by ϕ=− 1 ρ0 p dt . 21) 20 A review of the aircraft noise problem The perturbations in pressure, density and velocity in the sound wave are p = −ρ0 ∂ϕ , ∂t ρ = p a20 , vi = ∂ϕ . 23) ∂ 2ϕ − a20 ϕ = 0. 25) where k = ω/a0 is wave number (k = 2π /λ), = ∂2 ∂ x2 + ∂2 ∂ y2 + ∂2 ∂ z2 is the Laplacian, and x = x1 , y = x2 , z = x3 are Cartesian coordinates.
33) 24 A review of the aircraft noise problem where h = ρ/ρ0 . The asymptotic expansion of the inner solution is h(x, τ , M) = 1 + δ1 (M)σ1 (x, τ ) + δ2 (M)σ2 (x, τ ) + . . , a2 = 1 + δ1 (M)a21 (x, τ ) + . . , (0) (1) vi = vi (x, τ ) + δ1 (M)vi . . , where for M →0, the variables x, τ are ﬁxed. 34) δ2 (M) = M4 ; σ2 = ∂ 2 σ1 ∂τ 2 − ∂ 2 ∂σ1 ∂2 (1) (0) (0) (1) (0) (0) vi vj + vi vj + σ1 vi vj − 2 a . 35) where integration has been performed on the volume of turbulent ﬂow V(ξ ), and over bounding surfaces S = S1 + S0 + S∞ (Fig.
Aircraft noise propagation, exposure & reduction : assessment , prediciton and control by K Attenborough; V I Tokarev; Oleksandr Zaporozhets