Liquid Jet Atomization in a Compressible Gas Stream

Abstract

Alinearstabilityanalysishasbeen carried outfora viscousliquidjetissuedinto an inviscid movingcompressible gas medium with three-dimensional disturbances. The disturbances are allowed to grow both temporally and spatially. It is found that gas compressibility has a profound and signie cant ine uence on the stability of the liquid jet, especially athighMachnumbers. Itisalso shown thatthree-dimensionaldisturbancesplay animportantroleinthe atomization process, in particular, for e ows at high Weber numbers. Under certain conditions, three-dimensional sinuous disturbances even become more unstable than the corresponding two-dimensional axisymmetrical (varicose)disturbancesbecauseoftheeffectsofliquid viscosity. Effectsofotherparameterssuchasgas-to-liquid density ratio and gas velocity are also investigated. Nomenclature a = unperturbed liquid jet radius c = speed of sound for the gas phase In = modie ed Bessel function of the e rst kind with ordern i = p i1 Kn = modie ed Bessel function of the second kind with ordern k = axial wave number Ma = Ul/ c, the Mach number of the ambient gas with respect to a frame of reference m = ka n = azimuthal wave number n = unit vector normal to the liquid ‐gas interface, pointing into the gas phase P = pressure p = pressure perturbation qa = p fm 2 C[ / p (We) CimU] 2 M 2g q 2 = k 2 C(x CikUg) 2 / c 2