Stagnation lines

Cloud Water and Precipitation Collectors. Several methods have been developed for collecting cloud water samples (24-26). Probably the device most commonly used in warm clouds is the slotted rod collector developed by the Atmospheric Science Research Center at the State University of New York (SUNY) at Albany. Commonly known as the ASRC collector (25), this collector consists of an array of rods constructed from Delrin (a form of nylon). Each rod is hollow and has a slot located at its forward stagnation line. The rod radius determines the collection efficiency as a function of particle size, the rods are sized to collect cloud droplets but not submicrometer aerosol particles, and the 50% cutoff is calculated to be at about 3 xm. 

An important application of transpiration cooling is that of plane stagnation flow, as illustrated in Fig. 12-8. Solutions for the influence of transpiration on heat transfer in the neighborhood of such a stagnation line have also been worked out in Ref. 3, and the results are shown in Fig. 12-9. As would be expected, gas injection or suction can exert a significant effect on the temperature recovery factor for flow over a flat plate. These effects are indicated in Fig. 12-10, where the recovery factor r is defined in the conventional way as... 

If the condition (4) is satisfied, a steady state with the film covering the whole area is no longer possible. Instead, the film is split up into periodic bands (slicks) centred on the down-welling stagnation lines. We consider next such a down-welling zone in some more detail. 

We now consider a two-dimensional down-welling zone with a stagnation line at x = 0. The flow field below the boundary layer is taken to be... 

It is questionable to apply the experimental results of Mockros and Krone to a field situation. This is mainly because the role of the side walls and the bottom in the formation of the streaming filaments is not known. Another question is what happens when the substrate flow is non-uniform. A new experiment is needed, looking into these questions. One possibility is to make a down-welling zone with film accumulation symmetrically around the stagnation line, and making the experiment broad enough for side wall effects to be negligible. 

Formulas for calculating diffusion fluxes. The dimensionless total diffusion flux to a part of the surface of a particle (drop or bubble) between neighboring stagnation lines (points) rjk and rjk+i can be calculated by the formula [166]... 

Here 9k and 9k+ are the angular coordinates of stagnation lines (points) on the interface it is assumed that there are no stagnation lines and points in the interval Ok <9 < 9k+1. 

Note that in the case of axisymmetric linear shear flow to the surface of a spherical particle (drop or bubble), there are two isolated stagnation points 9 = 0 and 9 = it, as well as the stagnation line 9 = it/2. 

It was shown in [ 166] that in the two-dimensional problem of mass exchange between cylindrical bodies and a viscous flow, the diffusion layer consists of only two subregions W(3) and W(4) of total length L a Pe-1//9 (as Pe -> oo) the regions W(l) and W T> are absent. The diffusion wake in the vicinity of the stagnation lines on the surface of a solid particle has a similar structure. 

In Ref. 46, an ingenious set of transformations is employed to evaluate the recovery factor away from the stagnation line. The results for PP = 1 show a significant departure (= -10 percent for Pr = 0.7) from r(0) = Pr1 2. These values, however, do not agree with calculations performed in Ref. 49. Perhaps the discrepancy is due to the evaluation of r(0) in Ref. 46 by taking the derivative of a function. Slight errors in the function itself could easily account for a 10 percent error in the derivative. For accuracies of r(0) within a few percent [48], it is recommended that... 

Stagnation Line on a Cylinder in High-Speed Flow. The stagnation line on a uniform-temperature cylinder of infinite length with its axis either normal to the free stream or swept back at angle A is characterized by boundary layer similarity solutions with PP = 1. The solution in Ref. 16 of Eqs. 6.100-6.102 for Pp = 1 yields the correlation... 

Along the stagnation line of a swept cylinder, the recovery enthalpy is less than the stagnation enthalpy. Thus, the effect of surface mass transfer on the recovery factor, as shown in Fig. 6.25, should be considered in establishing the proper driving potential for the... 

FIGURE 18.20 Correlation of single-phase convection data downstream of the stagnation line. Reprinted from D. T. Vader, F. P. Incropera, and R. Viskanta, "Local Convective Heat Transfer from a Heated Surface to an Impinging Planar Jet of Water, International Journal of Heat and Mass Transfer 34, pp. 611-623, 1991, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, OX5 1GB, U.K. 

Forward stagnation line O Rear stagnation line... 

Coating For forward roll, coating, predicts stagnation line downstream of gap ... 

AC Electro-Osmotic Flow, Fig. 7 (a) Collection of E. coli bacteria in tap water along the stagnation lines of ACEO flow on An microelectrodes at low frequency (100 Hz) and moderate voltage (1 V). (b) Preferential... 

A stagnation graph is composed of two types of lines, vortical lines (later called center stagnation lines by Keith and Bader ) and saddle lines, interconversion being allowed at critical points where an index theorem is obeyed. This states that on going... 

Figure 11. Circulation near a stagnation line, i.e., a (2, 0) singular point in the plane of the drawing, perpendicular to the stagnation line a saddle line when the two nonzero eigenvalues are real, A2 = —Ai in case a, and a vortical line when the two eigenvalues are imaginary, A2 = —Ai = Ai, in case b.

Singularities, Stagnation Lines and Stagnation Graph of a Current Density Field... 

The topology of the 7 vector field deserves a careful and detailed investigation. Its most interesting features are observed in the proximity of an SP at which the modulus 7 vanishes. An SP is classified in terms of topological index i [85, 86], and of a (rank, signature) label [15, 55-57, 87-90]. A continuous, open or closed, path of SPs is referred to as stagnation line (SL), consisting of either vortex points (index = + 1), or saddle points (index = —1). 

A simple model of velocity vector field exhibiting branching of vortex and saddle stagnation lines has been considered by Gomes [56] via the system of differential equations... 

Fig. 7.3 Perspective view of the stagnation graph of the Gomes flow, Eq. (7.60), for z <2.5. The central stagnation line coincides with the z axis. Green (red) lines correspond to clockwise (anticlockwise) vortices in Eigs. 7.1 and 7.2, saddle lines are blue...

Fig. 7.22 The stagnation graph of five-membered cyclic compounds. Clockwise from top left 1,3-cyclopentadiene, p5urole, furan, and thiophene in the presence of a magnetic field perpendicular to the molecular plane. Diamagnetic (paramagnetic) vortices are represented by green (red) lines, and saddle lines are blue. All the stagnation lines lie on the Tcr plane of magnetic synunetry...

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