Stagnation plane

Thus, we can replace u00 in Equation (8.36) and apply it to both opposed and wind-aided cases. For upward or wind-aided spread the speed increases as cos (f> increases to the vertical orientation. For downward or opposed flow spread, the speed is not significantly affected by changes in until the horizontal inclination is approached for the bottom orientation (—90 < wind-aided as a stagnation plane flow results from the bottom. Figure 8.19 gives sketches of the... 

Equation (5-8) is applicable in the range v2isentropic expansion at about the same rate that increases and the product (T/3) is therefore approx constant. The integral v2... 

Hiemenz (in 1911) first recognized that the relatively simple analysis for the inviscid flow approaching a stagnation plane could be extended to include a viscous boundary layer [429]. An essential feature of the Hiemenz analysis is that the inviscid flow is relatively unaffected by the viscous interactions near the surface. As far as the inviscid flow is concerned, the thin viscous boundary layer changes the apparent position of the surface. Other than that, the inviscid flow is essentially unperturbed. Thus knowledge of the inviscid-flow solution, which is quite simple, provides boundary conditions for the viscous boundary layer. The inviscid and viscous behavior can be knitted together in a way that reduces the Navier-Stokes equations to a system of ordinary differential equations. 

Assuming that Ar is known, the governing equations represent a third-order boundary-value problem that demands three boundary conditions. Assume that z is measured from the stagnation plane. At the stagnation surface (z = 0), the no-slip condition requires that... 

Fig. 6.6 Comparison of two alternative stagnation-flow configurations. The upper illustration shows the streamlines that result from a semi-infinite potential flow and the lower illustration shows streamlines that result from a uniform inlet velocity issuing through a manifold that is parallel to the stagnation plane. Both cases are for isothermal air flow at atmospheric pressure and T = 300 K. In both cases the axial inlet velocity is u = —5 cm/s. The separation between the manifold and the substrate is 3 cm. For the outer-potential-flow case, the streamlines are plotted over the same domain, but the flow itself varies in the entire half plane above the stagnation surface. The stagnation plane is illustrated as a 10 cm radius, but the solutions are for an infinite radius.

Fig. 6.13 Comparison of streamlines from rotating-disk solutions at two rotation rates. Both cases are for air flow at atmospheric pressure and T = 300 K. The induced inlet velocity is greater for the higher rotation rate. In both cases the streamlines axe separated by 27tA4< = 1.0 x 10-6 kg/s. The solutions are illustrated for a 2 cm interval above the stagnation plane and a 3 cm radius rotation plane. The similarity solutions themselves apply for the semi-infinite half plane above the surface.

Fig. 13.12 Opposed-flow diffusion flame between parallel, axisymmetric, burner faces that are fabricated as honeycomb monoliths. As illustrated, the flame is positioned on the oxidizer side of the stagnation plane. However, depending on the flow conditions as well as the fuel and oxidizer composition, the flame may form on the fuel side of the stagnation plane.

Solve first the nonreacting problem for the cold flow without a flame. Based on the computed velocity profile, determine the position of the stagnation plane. In physical terms, explain the position of the stagnation plane. Estimate an effective strain rate for the cold flow. 

Plot and discuss the structure of the velocity profile, including the position of the new stagnation plane. Where is the flame relative to the stagnation plane Estimate the strain rate for the combusting flow. 

Under the conditions of turbulence, the time-averaged velocity field is symmetric with respect to the free stagnation plane, provided the flow rates from the two nozzles are equal. The mean axial velocity profile has a similar shape to the curve of uju ) vs x. The gradient of the time-averaged axial velocity takes the maximum at the stagnation plane, while it approaches zero near the nozzle. 

In this reactor, two jets are generated and directed towards each other so that they collide in a stagnation plane. This plane is fluid-mechanically unstable and produces stochastic fluctuations and intense mixing in liquid. 

When the two jets meet at a free stagnation plane, the strength of the generated stochastic fluctuations depend directly on the axial momentum of... 

FIGURE 9.19 Velocity pniffle in a capiDaiy showing the stagnation planes where the crJloidal particle velocity is measured during microelectrophoresis. 

Profiles of mean and root-mean-squared (rms) temperatures were measured at 1-millimeter intervals along the stagnation plane. The latter was identified by the zero mean axial velocity as described below, of the opposed flames with thermocouple junctions comprising butt-welded bare platinum with platinum-rhodium (13%) wires of 50-micrometer diameter, with an aspect ratio of approx-... 

Figure 6.5 presents measured profiles of the mean and rms temperature in the stagnation plane as functions of bulk velocity and separation. The single-brush... 

The images of the single-brush flame were complemented by profiles of temperature, velocity, and calculated strain rates at the stagnation plane (not shown here), and the effects of forcing amplitude and frequency on the reduction in the mean extinction strain rate close to the axis were quantified while previous results [15] were extended to include the effects of bulk velocity and separation on extinction times. The amplitude of imposed oscillations was quoted in terms of the rms of the axial velocity fluctuations at the nominal stagnation point normalized by the bulk velocity [14],... 

The opposed injection configuration provides a number of benefits. There is linear momentum cancellation between the two entrained gas jets, with the stagnation plane at the center of the tube. As a result, small droplets are not thrown against the walls, but are left to disperse throughout the tube. Excessive wall wetting is avoided in this... 

Different orientations of a prolate spheroid at the stagnation plane in strong (a) uniaxial extension and (b) uniaxial compression or equal biaxial extension. In biaxial flow the particle can take any orientation in the stagnation plane, resulting in a lower drag force. 

FIGURE 6.35 Streamlines and velocity profile of a two-dimensional stagnation (plane hyperbolic planar extensional) flow. 

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