Boundary velocity gradient

Mechanisms of Flame Stabilization. CRITICAL BOUNDARY VELOCITY GRADIENT. A flame stabilized at the port of a Bunsen burner does not actually touch the rim. There is a dark region, called the dead space, between the rim and the flame. Heat is removed and free radicals are destroyed by the solid surface the burning velocity is reduced to zero and the flame is quenched. Even beyond the dead space, where the flame is able to exist as a luminous reaction zone, the burning velocity only gradually rises to the value achieved at a distance from solid surfaces. 

There is a critical boundary velocity gradient for each flame, Qs (for flash-back) and... 

The boundary velocity gradients may be computed from the following expression ... 

Figure 16. Basis of critical boundary velocity gradients for flash-back and blow-off...

The stability of burner flames is well accounted for in terms of critical boundary velocity gradients. The way in which flameholdcrs stabilize supported flames in ducts... 

Increased Flame Stability. Oxygen-enhanced flames have higher flame speeds than air/fuel flames. This means that in order to prevent either flashback or flame extinguishment the minimum gas exit velocities for an OEC flame must be higher than those for an air/fuel flame. The potential for flashback is discussed further in Section 1.3.4.5. Harris et al.30 have defined the critical boundary velocity gradient for a cylindrical tube as follows ... 

FIGURE 1.24 Critical boundary velocity gradient for flashback vs. oxidizer composition for a stoichiometric premixed methane flame through a cylindrical tube. (Adapted from Harris, M. E. et al., in Third Symposium on Combustion, Flame and Explosion Phenomena, Williams Wilkens, Baltimore, 1949, 80.)... 

Because the Navier-Stokes equations are first-order in pressure and second-order in velocity, their solution requires one pressure bound-aiy condition and two velocity boundaiy conditions (for each velocity component) to completely specify the solution. The no sBp condition, whicn requires that the fluid velocity equal the velocity or any bounding solid surface, occurs in most problems. Specification of velocity is a type of boundary condition sometimes called a Dirichlet condition. Often boundary conditions involve stresses, and thus velocity gradients, rather than the velocities themselves. Specification of velocity derivatives is a Neumann boundary condition. For example, at the boundary between a viscous liquid and a gas, it is often assumed that the liquid shear stresses are zero. In numerical solution of the Navier-... 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Diffusion-blading loss. This loss develops because of negative velocity gradients in the boundary layer. Deceleration of the flow increases the boundary layer and gives rise to separation of the flow. The adverse pressure gradient that a compressor normally works against increases the chances of separation and causes significant loss. 

Initially it was assumed that no solution movement occurs within the diffusion layer. Actually, a velocity gradient exists in a layer, termed the hydrodynamic boundary layer (or the Prandtl layer), where the fluid velocity increases from zero at the interface to the constant bulk value (U). The thickness of the hydrodynamic layer, dH, is related to that of the diffusion layer ... 

A region outside the boundary layer in which the velocity gradient in a direction perpendicular to the surface is negligibly small and in which the velocity is everywhere equal to the stream velocity. 

The thickness of the boundary layer may be arbitrarily defined as the distance from the surface at which the velocity reaches some proportion (such as 0.9, 0.99, 0.999) of the undisturbed stream velocity. Alternatively, it may be possible to approximate to the velocity profile by means of an equation which is then used to give the distance from the surface at which the velocity gradient is zero and the velocity is equal to the stream velocity. Difficulties arise in comparing the thicknesses obtained using these various definitions, because velocity is changing so slowly with distance that a small difference in the criterion used for the selection of velocity will account for a very large difference in the corresponding thickness of the boundary layer. 

If at a distance a from the leading edge the laminar sub-layer is of thickness 5 and the total thickness of the boundary layer is 8, the properties of the laminar sub-layer can be found by equating the shear stress at the surface as given by the Blasius equation (11.23) to that obtained from the velocity gradient near the surface. 

The boundary conditions are as follows In Figure 3.2.2, z-axis component and r-axis component velocities are zero for (1) and (2), respectively. The gradients of other variables are zero for both the boundaries. The gradients of all variables are zero for (3) and (4). No slip condition and heat transfer from the flame kernel to the spark electrode are assumed for (5) and (6), at the surface of spark electrode. 

To scrutinize the sensitivity of the flame structure to the description of the outer-flow field, we compared the flame structure obtained from the two limiting boundary conditions at the extinction state, which can be considered to be the most aerodynamically and kinetically sensitive state of the flame for a given mixture concentration, and demonstrated that they were basically indistinguishable from each other. This result thus suggests that the reported discrepancies in the extinction stretch rates as mentioned in the work by Kee et al. [19] are simply the consequences of the "errors" associated with the evaluation of the velocity gradients. 

For large values of 6, Manohar [42], and Banks [4] solved the boundary layer Eqs. (2)-(5) numerically with a finite difference method. Manohar s results for the meridional and azimuthal velocity gradients on the spherical surface have been curve-fitted by Newman [45] and Chin [18] to follow the following equations in the regime of 0 < 9 < 7t/2 ... 

When velocity gradients are small, for example, near the boundary layer separation point and at the rear of a cylinder in separated flow, Eq. (33) is inaccurate. The separation point was determined with an accuracy of 1 degree by using twin strip electrodes of 125 /im length, separated by... 

The velocity of liquid flow around suspended solid particles is reduced by frictional resistance and results in a region characterized by a velocity gradient between the surface of the solid particle and the bulk fluid. This region is termed the hydrodynamic boundary layer and the stagnant layer within it that is diffusion-controlled is often known as the effective diffusion boundary layer. The thickness of this stagnant layer has been suggested to be about 10 times smaller than the thickness of the hydrodynamic boundary layer [13]. 

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