Shear layer

In shear layers, large-scale eddies extract mechanical energy from the mean flow. This energy is continuously transferred to smaller and smaller eddies. Such energy transfer continues until energy is dissipated into heat by viscous effects in the smallest eddies of the spectrum. 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

We have now to go one step further and to build stellar evolution models where the transport of angular momentum will be followed self-consistently under the action of meridional circulation, shear turbulence, and internal gravity waves. In this path some important aspects still need to be clarified Can we better describe the excitation mechanisms and evaluate in a more reliable way the quantitative properties of the wave spectra What is the direct contribution of 1GW to the transport of chemicals, especially in the dynamical shear layer produced just below the convective envelope by the wave-mean flow interaction What is the influence of the Coriolis force on IGW How do 1GW interact with a magnetic field Work is in progress in this direction. 

A two-color pyrometer has been used along with the phase-Doppler anemometer to simultaneously measure the local velocity and size of kerosene droplets and the temperature of burning soot mantle in a swirl burner.[648] The measurements were conducted within the flame brush that develops in the shear layer of a swirl-stabilized, gas-supported kerosene flame with a swirl number of about 0.19 and potential heat releases of 10.6 and 15.5 kW, respectively. The results showed that the maximum burning fraction of the droplets occurs adjacent to the region denoted as gas flame but the value ranges from 20 5 to 40 5% depending on the axial station, and decreases sharply across the shear layer. The flame mantle temperature was found to be independent of droplet diameter, which agrees with previous results in the literature. 

Linear-eddy modeling of turbulent transport. II Application to shear layer mixing. 

Figure 1.2 Schematic of a compact combustor using countercurrent shear layer (a) and comparison of measured strain rate fields in a single-stream (6) and countercurrent (c) shear layers [9]...

Strykowski, P. J., A. Krothapalli, and S. Jendonbi. 1996. The effect of connterflow on the development of compressible shear layers. J. Fluid Mechanics 308 63-96. 

Figure 6.1 shows the apparatus diagram. The diffusion flame burner consisted of an air plenum with an exit diameter of 22 mm, forced at a Strouhal number of 0.73 (100 Hz) by a single acoustic driver, and a coaxial fuel injection ring of diameter 24 mm, fed by a plenum forced by two acoustic drivers at either 100 Hz (single-phase injection) or 200 Hz (dual-phase injection). The fuel was injected circumferentially directly into the shear layer and roll-up region for the air vortices. In addition, this fuel injection was sandwiched between the central air flow and the external air entrainment. Thus the fuel injection was a thin cylindrical flow acted upon from both sides by air flow. 

Broadwell, J. E., and R. E. Breidenthal. 1982. A simple model of mixing and chemical reaction in a turbulent shear layer. J. Fluid Mechanics 125 397-410. 

Ho, M., and P. Huerre. 1984. Perturbed free shear layers. Annual Reviews Fluid Mechanics 16 365. 

McManus, K.R., V. Vandsburga, and C.T. Bowman. 1990. Combustor performance enhancement through direct shear layer excitation. Combustion Flame 82 75-92. 

Figure 7.8 Fourier spectrum of radial velocity fluctuations in the shear layer for unseeded flow and fully developed flow wifh microexploding droplets 1 — no par tides 2 — particles...

The flow involves fuel, F, issuing from a central slot of width D with an oxidizer, O, co-flow with both streams at the reference temperature, Tq. A global single-step, irreversible, exothermic chemical reaction of the type F + rO —> (1 -f r)P with an Arrhenius reaction rate coefiicient is assumed. A hot layer of combustion products, P, at the inlet serves to separate the fuel and oxidizer streams and acts as an ignition source. The inlet conditions for the velocity, temperature, and composition are shown in Fig. 10.2. The ratio of the inlet velocities of the fuel to oxidizer streams is chosen as 4. Inlet velocity forcing is used to induce early roll-up and pairing of the jet shear layer vortices. 

Kaplan, C. R., S. W. Back, E. S. Oran, and J. L. Ellzey. 1994. Dynamics of strongly radiating unsteady ethylene jet diffusion flame. Combustion Flame 96 1-22. Kennedy, C.A., and M. H. Carpenter. 1994. Several new numerical methods for compressible shear-layer simulations. Applied Numerical Methods 14 397-433. Baum, M., T. Poinsot, and D. Thevenin. 1994. Accurate boundary conditions for multicomponent reactive flows. J. Comput. Phys. 116 247-61. 

The initial conditions for the velocity components are set up so that there is a tubular shear layer aligned along the 2 -direction at time t = 0. The tv-velocity has a top-hat profile with a tan-hyperbolic shear layer. Stream wise and azimuthal perturbations are introduced to expedite roll-up and the development of the Widnall instability. The details can be found in [7]. The initial velocity field is made divergence-free using the Helmholtz decomposition. The size of the computational domain (one periodic cubical box) is 4do on each side. 

Dimotakis, R E. 1991. Turbnlent free shear layer mixing and combustion. Prog. Astro. Aero. 137 265-340. 

As the reactant elements pass through the shear layer, they pick up and convect turbulent fluctuations to the flame. There is no constraint that the flame speed and radial velocity be uniform along the axis however, since the flame... 

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