Vortex strength

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

The predicted flame speeds. Equations 4.2.1 and 4.2.3, are in qualitative agreement with the flame speed determined by McCormack et al. [3] in the fact that the flame speed increases with an increase of vortex strength, and that the flame speed is further raised up if pure oxygen... 

The stroke ratio Ljd = U/((od) is equal to the inverse of the Strouhal number. However, the limitation of stroke ratio definition is the assumption of slug-velocity profile. Holman et al. [3] discussed the formation criteria of synthetic jet based on both numerical simulation and experiment. They observed that the vortex ring needs to withstand the suction velocity during ingestion stroke which is a function of the vortex strength. From dimensional reasoning, they proposed the following criterion for jet formation ... 

Vortex strength Cocurrent and countercurrent flow patterns Bed pressure drop Average density... 

This singular integral equation, with the Cauchy kernel l/(x- ), governs the vortex strength g(Q. The PV indicates that the integral is improper and must be evaluated using the limit process in Example 2-5. 

Physical significance of vortex strength. Let us take the derivative of Equation 3-21 with respect to x. Then, it follows that... 

Thus, the singular integral equation for the vortex strength g(x) becomes +1... 

Once this expression is substituted in Equation 3-25 for the vortex strength, the final expression for g(x) is obtained by choosing the circulation y consistently with Equation 3-28, ealling for vanishing velocity swirl in the farfield. 

This remarkably simple result shows that for a given physical situation for which and are fixed, the total product generated within a time t increases with stirring as where Pis the vortex strength generated in the stirring process. 

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