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22.6 Dynamic Drag Model Theory

Accurate determination of droplet drag coefficients is crucial for accurate spray modeling. FLUENT provides a method that determines the droplet drag coefficient dynamically, accounting for variations in the droplet shape.

The dynamic drag model is applicable in almost any circumstance. It is compatible with both the TAB and wave models for droplet breakup. When the collision model is turned on, collisions reset the distortion and distortion velocities of the colliding droplets.

Many droplet drag models assume the droplet remains spherical throughout the domain. With this assumption, the drag of a spherical object is determined by the following [ 218]:

 C_{d, \rm sphere} = \left\{ \begin{array}{cl} 0.424 & {\rm R... ...{\rm Re}^{2/3}\right) & {\rm Re} \leq 1000 \end{array} \right. (22.6-1)

However, as an initially spherical droplet moves through a gas, its shape is distorted significantly when the Weber number is large. In the extreme case, the droplet shape will approach that of a disk. The drag of a disk, however, is significantly higher than that of a sphere. Since the droplet drag coefficient is highly dependent upon the droplet shape, a drag model that assumes the droplet is spherical is unsatisfactory. The dynamic drag model accounts for the effects of droplet distortion, linearly varying the drag between that of a sphere (Equation  22.6-1) and a value of 1.54 corresponding to a disk [ 218]. The drag coefficient is given by

 C_d = C_{d, \rm sphere}(1 + 2.632y) (22.6-2)

where $y$ is the droplet distortion, as determined by the solution of

 \frac{d^2y}{dt^2} = \frac{C_F}{C_b}\frac{\rho_g}{\rho_l}\fra... ...sigma}{\rho_l r^3}y -\frac{C_d \mu_l}{\rho_l r^2}\frac{dy}{dt} (22.6-3)

In the limit of no distortion ( $y=0$), the drag coefficient of a sphere will be obtained, while at maximum distortion ( $y=1$) the drag coefficient corresponding to a disk will be obtained.

Note that Equation  22.6-3 is obtained from the TAB model for spray breakup, described in Section  22.7.2, but the dynamic drag model can be used with either of the breakup models.

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© Fluent Inc. 2006-09-20