Investigation of a High-Mach-Number Overexpanded Jet Using Large-Eddy Simulation
a n = relative contribution of azimuthal modes n c = local sound speed c1 = ambient field sound speed f = frequency fc = cutoff frequency fshock = central frequency of the broadband shockassociated noise fup = frequency of the upstream-propagating shockassociated noise LVS = first shock length from vortex sheet, 2 M j 1 rj= 1, 1 2:40483 L1 = first shock length measured on the jet axis Ma = acoustic Mach number Mc = convection Mach number Me = exit Mach number Mj = equivalent fully expanded exit Mach number, uj=c1 n = azimuthal mode pe = exit static pressure pj = equivalent fully expanded exit static pressure p0 = fluctuating static pressure hpi = mean static pressure Re = Reynolds number based on exit conditions re = nozzle radius rj = equivalent fully expanded nozzle radius Stc = cutoff Strouhal number Ste = Strouhal number based on exit conditions Stup = Strouhal number of the upstream-propagating shock-associated noise Te = exit temperature uaxis = centerline mean axial velocity uc = convection velocity ue = exit velocity uj = equivalent fully expanded exit velocity huzi = mean axial velocity hu02 z i = mean-square axial velocity fluctuations hu02 z in = mean-square axial velocity fluctuations due to mode n juz j Ste; n = two-dimensional power spectral densities z1 = first shock location on the jet axis = specific heat ratio r = mesh size in the radial direction z = mesh size in the axial direction = boundary-layer thickness in the pipe nozzle