P. vortex

Numerous studies for the discharge coefficient have been pubHshed to account for the effect of Hquid properties (12), operating conditions (13), atomizer geometry (14), vortex flow pattern (15), and conservation of axial momentum (16). From one analysis (17), the foUowiag empirical equation appears to correlate weU with the actual data obtained for swid atomizers over a wide range of parameters, where the discharge coefficient is defined as — QKA (2g/ P/) typical values of range between 0.3 and 0.5. 

Above Re = 10 the vortex shedding is difficult to see in flow visualization experiments, but velocity measurements still show a strong spectral component at St = 0.2 (Panton, p. 392). Experimental data suggest that the vortex street disappears over the range 5 X 10 < Re < 3.5 X 10 , but is reestablished at above 3.5 X 10 (Schhchting). 

For Nr, > 1000, the properly baffled tank is turbulent throughout. Nq and P, are independent of Nr,. If the tank is not baffled, a forced vortex dominates the flow in the vessel. 

Flame speed versus vortex strength. (From McCormack, P.D., ScheUer, K., Mueller, G., and Tisher, R., Combust. Flame, 19,297,1972.)... 

He considered that the rapid flame propagation could be achieved with the same mechanism as vortex breakdown. Figure 4.2.2 schematically shows his vortex bursting mechanism [4,5]. When a combustible mixture rotates, Ihe pressure on the axis of rotation becomes lower than the ambient pressure. The amount of pressure decrease is equal to max in Rankine s combined vor-fex, in which p denotes fhe unburned gas density and Vg denotes the maximum tangential velocity of the vortex. However, when combustion occurs, the pressure on the axis of rofafion increases in the burned gas owing to the decrease in the density, and becomes close to the ambient pressure. Thus, there appears a pressure jump AP across the flame on fhe axis of rotation. This pressure jump may cause a rapid movement of the hot burned gas. By considering the momentum flux conservation across the flame, fhe following expression for the burned gas speed was derived ... 

Further measurements on the flame speed have been obtained with the use of a rotating tube [11] and vortex ring combustion [12]. Figure 4.2.4 shows the flame speed in vortex rings [12]. The values of slope in the V( -plane is nearly equal to unity for the near stoichiometric methane/air mixtures. Thus, this value is much lower than the predictions of JPi/P, and flPn/P >. 

Vector profiles of (a) cold vortex ring and (b) burning vortex ring (Dq = 60mm, P = 0.6MPa, stoichiometric mixture). Insets show the relative position of the PIV laser sheet to (a) the vortex ring and (b) the flame. 

Vector profile of vortex ring combustion, showing induced velocities along the vortex core. (Lean propane/air mixture, equivalence ratio O = 0.8, Do = 60 mm, P= 0.6 MPa, dotted lines show the flame front taken with the ICCD camera. The right inset shows the relative position of the PIV laser sheet relative to the flame.)... 

T.J. Poinsot, A.C. Trouv D.P. Veynante, S.M. Candel, and E.J. Esposito. Vortex driven acoustically coupled combustion instabilities. /. Fluid Mech., 177 265-292,1987. 

In more modern times the epoxidation of (18) in a confined vortex (14,000 r.p.m. in a turbine) has been reportedi2d to give a product with a liny optical rotation, but doubt has been cast on this observation... 

Fig. 2. Mixing in the vortex mixing flow with increasing periods of flow (P). The flow is time periodic with each cylinder rotating alternately for a fixed time period (Jana, Metcalfe and Ottino, 1994).

An acetone powder of P. homomalla was subsequently used to generate allene oxide 64 from exogenous 8P-HPETE [91]. This highly unstable compound (t1/2 = ca. 15 s at 0 °C, pH 7.4) was obtained by performing the biosynthesis at low temperature (0 °C) for 2 min in a vortexed emulsion of pH 6 buffer and pentane. Under these conditions, the allene oxide partitioned into the pentane where it was relatively protected from hydrolysis. HPLC analysis of the... 

Pagni, P.J., Pool fire vortex shedding frequencies, Applied Mechanics Review, 1990, 43, 153-70. 

For example, the vortex-stretching term is a triple-correlation term that corresponds to the rate at which dissipation is created by spectral energy passing from the inertial range to the dissipative range of the energy spectrum (see (2.75), p. 43). Letting /cdi 0.1 denote... 

The wave function of a singly quantized rotational vortex centered on the cylinder axis is ka = kA exp where

azimuthal angle around the... 

Gutmark, E., T.P. Parr, K. J. Wilson, K.H. Yu, R. A. Smith, D.M. Hanson-Parr, and K. C. Schadow. 1996. Compact waste incinerator based on vortex combustion. Combustion Science Technology 121 333-49. 

Significant improvement of the combus-tion energy release was obtained by introduc-ing a dual-fuel injection scheme. Fuel is in-P jected twice per air vortex shedding. Fig-... 

Post, M. E., and L. P. Goss. 1993. Two-color particle-imaging velocimetry in vortex structures. 31st Aerospace Sciences Meeting Proceedings. AIAA Paper No. 93-0412. 

Kailasanath, K., J.H. Gardner, J. P. Boris, and E. S. Oran. 1987. Numerical simulations of acoustic-vortex interactions in a central-dump ramjet combustor. J. Propulsion Power 3 525-33. 

Givi, P. 1994. Spectral and random vortex methods in turbulent reacting flows. In Turbulent reacting Bows. Eds. P. A. Libby and F.A. Wilhams. London, UK Academic Press. 475-572. 

Grinstein, F.F., E. G. Gutmark, T. P. Parr, D.M. Hanson-Parr, and U. Obey-sekare. 1996. Streamwise and spanwise vortex interaction in an axisymmet-ric jet. A computational and experimental study. J. Physics Fluids 8 1515-24. 

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