Journal of Fluid Mechanics

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Stabilizing effect of surrounding gas flow on a plane liquid sheet

OUTI TAMMISOLAa1, ATSUSHI SASAKIa2, FREDRIK LUNDELLa1a3 c1, MASAHARU MATSUBARAa2 and L. DANIEL SÖDERBERGa3a4

a1 Linné Flow Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

a2 Mechanical Systems Engineering, Shinshu University, Nagano 380-8553, Japan

a3 Wallenberg Wood Science Center, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

a4 Innventia AB, Box 5604, SE-114 86 Stockholm, Sweden

Abstract

The stability of a plane liquid sheet is studied experimentally and theoretically, with an emphasis on the effect of the surrounding gas. Co-blowing with a gas velocity of the same order of magnitude as the liquid velocity is studied, in order to quantify its effect on the stability of the sheet. Experimental results are obtained for a water sheet in air at Reynolds number Rel = 3000 and Weber number We = 300, based on the half-thickness of the sheet at the inlet, water mean velocity at the inlet, the surface tension between water and air and water density and viscosity. The sheet is excited with different frequencies at the inlet and the growth of the waves in the streamwise direction is measured. The growth rate curves of the disturbances for all air flow velocities under study are found to be within 20% of the values obtained from a local spatial stability analysis, where water and air viscosities are taken into account, while previous results from literature assuming inviscid air overpredict the most unstable wavelength with a factor 3 and the growth rate with a factor 2. The effect of the air flow on the stability of the sheet is scrutinized numerically and it is concluded that the predicted disturbance growth scales with (i) the absolute velocity difference between water and air (inviscid effect) and (ii) the square root of the shear from air on the water surface (viscous effect).

(Received May 02 2010)

(Revised August 30 2010)

(Accepted November 17 2010)

(Online publication February 18 2011)

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    Key words:

    • instability control;
    • interfacial flows (free surface);
    • jets

    Correspondence:

    c1 Email address for correspondence: fredrik@mech.kth.se

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