Spray Penetration in a Turbulent Flow

Analytical expressions for mass concentration of liquid fuel in a spray are derived taking into account the effects of gas turbulence, and assuming that the influence of droplets on gas is small (intitial stage of spray development). Beyond a certain distance the spray is expected to be fully dispersed. This distance is identified with the maximum spray penetration. Then the influence of turbulence on the spray stopping distance is discussed and the rms spray penetration is computed from a trajectory (Lagrangian) approach. Finally, the problem of spray penetration is investigated in a homogeneous two-phase flow regime taking into account the dispersion of spray away from its axis. It is predicted that for realistic values of spray parameters the spray penetration at large distances from the nozzle is expected to be proportional to t2/3 (in the case when this dispersion is not taken into account this distance is proportional to t1/2). The t2/3 law is supported by experimental observations for a high pressure injector.

[1]  Martin R. Maxey,et al.  The motion of small spherical particles in a cellular flow field , 1987 .

[2]  A. Lefebvre.  Atomization and Sprays , 1988 .

[3]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[4]  Dennis L. Siebers,et al.  Liquid-Phase Fuel Penetration in Diesel Sprays , 1998 .

[5]  Jean-Pierre Minier,et al.  PROBABILITY DENSITY FUNCTION MODELING OF DISPERSED TWO-PHASE TURBULENT FLOWS , 1999 .

[6]  S. Pope.  Lagrangian PDF Methods for Turbulent Flows , 1994 .

[7]  E. Peirano,et al.  The pdf approach to turbulent polydispersed two-phase flows , 2001 .

[8]  Morgan Heikal,et al.  A model for fuel spray penetration , 2001 .

[9]  David E. Stock,et al.  Particle Dispersion in Flowing Gases—1994 Freeman Scholar Lecture , 1996 .

[10]  Dennis L. Siebers,et al.  Scaling Liquid-Phase Fuel Penetration in Diesel Sprays Based on Mixing-Limited Vaporization , 1999 .

[11]  John R. Fessler,et al.  Preferential concentration of particles by turbulence , 1991 .

[12]  J. C. R. Hunt,et al.  Settling of small particles near vortices and in turbulence , 2001, Journal of Fluid Mechanics.

[13]  M. Maxey.  The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields , 1987, Journal of Fluid Mechanics.

[14]  Olivier Simonin,et al.  Eulerian Prediction of the Fluid/Particle Correlated Motion in Turbulent Two-Phase Flows , 1993 .

[15]  J. Naber,et al.  Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays , 1996 .

[16]  J. Minier,et al.  On the Lagrangian turbulent dispersion models based on the Langevin equation , 1998 .

[17]  M. Maxey,et al.  Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence , 1993, Journal of Fluid Mechanics.

[18]  G. Csanady.  Turbulent Diffusion in the Environment , 1973 .

[19]  Clayton T. Crowe,et al.  On Models for Turbulence Modulation in Fluid-Particle Flows , 2000 .

[20]  Clayton T. Crowe,et al.  Review—Numerical Models for Dilute Gas-Particle Flows , 1982 .

[21]  Julian C. R. Hunt,et al.  Induced air velocity within droplet driven sprays , 1994, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.