J054756Far-field drag extraction has the advantage over near-field integration of providing a phenomenological breakdown of drag. A decomposition into components linked to shock waves, viscous interactions, and lift-induced vortices is straightforward for steady flows. A formulation based on thermodynamic considerations is used at ONERA-The French Aerospace Lab and by its partners, but it is restricted to steady cases. A generalization to unsteady flows of the Van der Vooren formulation has been developed and tested on three unsteady cases previously. The proposed method allowed the breakdown of drag into the three usual components only; however, the induced drag coefficient remained ill-defined. This unsteady formulation is here modified to better express the induced drag. A new drag component is identified as a propagation and acoustics contribution. The new formulation is then applied to complex cases: two-dimensional and three-dimensional pitching cases, and an OAT15A profile subject to buffet simulated by zonal detached-eddy simulation computations.new propagation and acoustics drag D sp = spurious drag D ui = unsteady induced drag D v = viscous drag D vw = profile drag D w = wave drag H = stagnation enthalpy; h q 2 ∕2 h = enthalpy i = freestream direction vector k = reduced frequency for the pitching velocity ω; 2kM ∞ ∕c M = Mach number n = normal vector pointing outside the flow domain p = static pressure p i = stagnation pressure p1 γ − 1∕2M 2 γ∕γ−1 q = velocity vector Re = Reynolds number r = gas constant S a = surface of the body S cd = complementary downstream wake plane; S d \ S wd ∪ S vd S d = downstream wake plane S e = outer surface of the fluid volume S v = surface for the integration of viscous drag S vd= downstream wake plane of the streamtube enclosing the body and its boundary layer S w = surface for the integration of wave drag S wd = downstream wake plane of the streamtube enclosing the shock s = entropy T = temperature t = time u, v, w = velocity components in an inertial reference frame u irr = axial velocity under irreversible flow assumptions= volume enclosed within S v V w = volume enclosed within S w V wd = volume downstream of V w α = angle of attack γ = ratio of specific heats ρ = density τ = deviatoric stress tensor τ x = longitudinal stress vector; τ · i Subscript ∞ = freestream state
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