Stagnation flow numerical solution

The dimensions of the attached wake are shown in Figs. 5.6, 5.7, and 5.8. The various numerical solutions agree closely with flow visualization results of Taneda (T2), although other workers (K2) report separation slightly closer to the rear. The separation angle, measured in degrees from the front stagnation point, is well approximated by... 

Develop a numerical solution to describe the axisymmetric, semi-infinite, isothermal, stagnation flow of air with strain rates in the range 1/s < a < 1000/s. Solve the problem in physical variables (i.e., not nondimensional) using constant properties evaluated at T = 300 K. 

When flow occurs about a sphere the solution to tins forced convection mass transfer problem is quite complex because of the complexity of the flow field. At low flow rates (creqiiiig flow) a laminar boundary layer exists about the sphere which separates from die surface at an at ular porition and moves lowani the forward stagnation point as the flow rate increases. Wake fimnation occurs st the tear of the sphere. At still higher flow rates transition to a turbulent boundary layer occurs. Solutions to the problem of mass transfer during creeping flow about a sphere (Re < 1) have been developed by a nombw of authors with the numerical solutions of Brian and Hales being perhaps the most extensive. Their result is... 

It is often important to predict and understand the flame extinction phenomenon in stagnation or opposed flows. As discussed briefly in Sect. 17.5 and illustrated in Fig. 17.11, the extinction point represents a bifurcation where the steady-state solutions are singular. Thus direct solution of the discrete steady problem by Newton s method necessarily cannot work because the Jacobian is singular and cannot be inverted or factored into its LU products. Moreover, in some neighborhood around the singular point, the numerical problem becomes sufficiently ill-conditioned as to make it singular for practical purposes. 

Results obtained using equation (27) were compared with two exact solutions to the Stokes equation. Flrst the solution for a simple shearing motion was checked Wj - -x., W. 0. Secondly, the Stokes stagnation point flow field was checked = x Xp W > -1/2x 2. g th solutions were checked in the bounded domain shown in figure (2). Agreement between the exact and numerical values was always within 3%. 

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