Temperature Effects on Convection Speed and Steepened Waves of Temporally Developing Supersonic Jets

Pierre Pineau (1) , Christophe Bogey (1)

1 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique

Temperature effects on the convection speed of large-scale structures in supersonic temporally-1 developing jets and on the steepened aspect of the acoustic waves generated by these structures 2 are investigated. For that, one isothermal jet at Mach 2 and four others at static temperatures 3 equal to 2 or 4 times that of the ambient medium are simulated at either the same exit velocity 4 or Mach number as the isothermal jet. For all temporally-developing jets, steepened acoustic 5 waves are emitted in the near field, leading to significant values of the pressure skewness and 6 kurtosis factors. Using conditional averages, their formation is directly linked to the supersonic 7 motion of large-scale structures at a convection speed whose ratio with the jet velocity is shown 8 to decrease with temperature. At a higher temperature, this leads to the generation of less 9 skewed acoustic waves for a constant jet velocity. For a constant Mach number, however, this 10 decrease is compensated by the rise of the jet speed, leading to steeper acoustic waves at a 11 higher temperature. Therefore, the modification of the steepened aspect of near-field acoustic 12 waves appears to be related to the change in the convection speed in both cases. 13 Nomenclature 14 T = temperature p = pressure ρ = density u = velocity a = speed of sound M = Mach number F = Net thrust m = Mass flow rate µ = dynamic viscosity ν = kinematic viscosity * PhD, post-doctoral fellow at CNES, [e-mail] † CNRS Research Scientist, AIAA senior member r s = specific ideal gas constant γ = ratio of specific heats r = radial coordinate θ = azimuthal coordinate z = axial coordinate t = time ∆r = radial mesh spacing ∆θ = azimuthal resolution ∆z = axial mesh spacing D = jet diameter r 0 = jet radius Re D = diameter-based Reynolds number δ θ = shear-layer momentum thickness δ θ = momentum thickness growth rate δ θ,inc = momentum thickness growth rate for an incompressible mixing layer δ 05 = jet half-width α = Mach wave radiation angle Subscripts ∞ = ambient quantity j = initial value of the jet parameters c = potential core closure axis = centerline quantity cond = conditionally averaged trig = conditional averages trigger

Domaines: Sciences de l'ingénieur [physics]

Pierre Pineau, Christophe Bogey. Temperature Effects on Convection Speed and Steepened Waves of Temporally Developing Supersonic Jets. AIAA Journal, 2020, 58 (3), pp.1227-1239. ⟨10.2514/1.J058589⟩. ⟨hal-02504344⟩