Axisymmetric jets

Experimental studies have shown that velocity distribution in the cross-section of the directing jet can be described by the same equation as those in the axisymmetric jet in a cross-draft,... 

Gendrikson, V. A., and Y. V. Ivanov. 1973. Some regularities of axisymmetric jets supplied at an angle to the cross-draft. In Proceedings of the Tashkent Polytechnical Institute, vol. 101, pp. 184-1.98. 

The cold jet theory was applied in the region between the nozzle and the edge of lifted flame, which, for the axisymmetric jets, has the following similarity solutions [10,11] ... 

Y. -C. Chen and R. W. Bilger, Stabilization mechanism of lifted laminar flames in axisymmetric jet flows. Combust. Flame 122 377-399, 2000. 

Sanders, J. P. H. and I. Gokalp (1998). Scalar dissipation rate modelling in variable density turbulent axisymmetric jets and diffusion flames. Physics of Fluids 10, 938-948. 

For a typical case, an axisymmetric jet with a mean velocity of 100 m/s flows through the cylindrical inlet of diameter D into a cylindrical combustion chamber of twice the diameter. An annular or central exit at the end of the combustion chamber is modeled to produce choked flow. Particles are injected from the inlet-combustor junction with a streamwise velocity of 50 m/s and zero radial velocity. If the number of particles is small (that is, for low-mass loadings), the effect of the particles on the flow can be neglected. Still the flow has an effect on the particles that depends on parameters such as the size and density of the particles. Such systems are called one-way coupled systems and are discussed next. 

Figure 10.9 The axisymmetric free turbulent jet. The initial region of the axisymmetric jet, extending to 5-10 nozzle diameters, consists of an undisturbed cone of nozzle fluid surrounded by the shear layer. For nucleation-controlled growth, particle formation is conlined to the shear layer.

Turbulent jet. Now consider a turbulent plane jet. Estimates show that the turbulent viscosity in this case is constant within every cross-section of the jet (but varies along the jet axis, just as was the case for an axisymmetric jet). In the boundary layer approximation, the solution of the corresponding hydrodynamic problem results in the following fluid velocity components [395,427] ... 

Grinstein, F. F., E. J. Gutmark, T. P. Parr, D. M. Hanson-Parr, and U. Obeysekare. 1996. Streamwise and spanwise vortex interaction in an axisymmetric jet. A Computation and Experimental Study. Physics Fluids 8(6) 1515-24. 

Zhao, W., S. H. Frankel, and L. Mongeau. 2000. Effect of spatial filtering on sound radiation from a subsonic axisymmetric jet. AIAA J. 38( 11 ) 2032-39. 

Prevost, f., Boree, J., Nuglisch, H.J., Chamay, G. Measurements of fluid/particle correlated motion in the far field of an axisymmetric jet. Int. J. Multiphase Flow, 22, 685-701 (1996)... 

Other boundary conditions depend on the particular problem. For instance, for the instability of an axisymmetric jet, the axisymmetric condition oti the axis of the jet is applied. 

The pressure boundary condition is the Yotmg-Laplace equation (1.3) and (1.4), which for an axisymmetric jet can be written as ... 

Fig. 18.13 Spike behavior at the tip of an electrified column, (a) Cross-sectional view of a 2D jet [3] showing the effect of initial deformation and (b) side view of an axisymmetric jet [70] showing the effect of charging level. The jet is disturbed at ka= 1.3 and bla = 10 (Courtesy of Elsevier)...

The energy spectrum, however, comprises fluctuating motions with a spectrum of timescales, and a single timescale approach is unlikely to be adequate under all circumstances. Consequently, the model has been found to perform less satisfactorily in a number of flow situations, including separated flows, streamline curvature, swirl, rotation, compressibility, axisymmetrical jets, etc. 

In this section we describe some models for solving diffusion flames as the flamelet technique, a model for an axisymmetric jet diffusion flame and a model for a plume. Figure 5.7 shows the stracture of a diffusion flame. 

In what follows we present the equations and boundary conditions for the problems which are addressed here, namely axisymmetric jets (two-phase generalizations are straightforward) and spherically symmetric drops or bubbles. Before presentation of the mathematical models, we also give a brief description of the applications and what we hope too understand by the theoretical studies. For the sake of brevity, the elements of tensor algebra which are needed in deriving interfacial conditions will be stated and described as needed. For general descriptions the reader is referred to the texts by Aris [1], Edwards et al. [18] and McConnell... 

In this Section we consider the stability of some exact solutions of the governing equations for axisymmetric jets. The viscous system is (2)-(5) along with the inerfacial boundary conditions given in Section 2.1. It is clear that a perfectly cylindrical interface (r = i in dimensional terms) along with a velocity field u = ([/, 0,0) where i7 is a constant, is an exact solution of the equations of motion and boundary conditions. This is clearly true also for inviscid flows having /z = 0. (In fact, inviscid flows allow exact solutions for the velocity field of the form u = ([/(r),0,0) with U[r) any suitably differentiable function.)... 

Little has been published on the effect of Reynolds number on extrudate swell of liquids from fully three-dimensional dies. However, its effect on two-dimensional extrudate swell of a Newtonian fluid has been well characterized [1-4]. The influence of Reynolds number on the final die swell ratio for both planar jets (i.e., the thickness of the extrudate divided by the width of the channel) and axisymmetric jets (i.e., the diameter of the jet divided by that of the tube) are summarized in Fig. 1. In both cases, swell is greater than 1 for low Reynolds numbers but decreases to values less than 1 at high Reynolds numbers. As Reynolds number approaches infinity, the die swell ratios for the axisymmetric and planar jets approach the asymptotic values of /3/2 and 5/6, respectively [5,6]. 

The effects of the Reynolds number on the extrusion of Newtonian fluid from square and rectangular dies has been considered. As with planar and axisymmetric jets, extrudates from three-dimensional dies swell at low Reynolds numbers but contract at high ones. Depending on its aspect ratio, limiting die swell from the rectangle varies that of the square (0.7255) and that of two-dimensional planar case (0.8333). Wall slip reduces die swell and in the cases of perfect slip, completely eliminates it. 

Huber, A. M., Viskanta, R., 1994. Effect of jet-jet spacing on convective heat transfer to confined, impinging arrays of axisymmetric jets. Int. J. Heat Mass Transfer 37 2859-2869. 

The improved cell utilizes axisymmetric jets of feed gas impinging upon both sides of the wafer to develop a highly turbulent field over most of the wafer surface. This enables global reaction rates to approximate intrinsic reaction rates at high flow-rates and in the absence of pore diffusion. 

Panchapakesan NR, Lumley JL (1993) Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet. J Fluid Mech 246 197-223... 

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