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22.8.5 The Effervescent Atomizer Model

Effervescent atomization is the injection of liquid infused with a super-heated (with respect to downstream conditions) liquid or propellant. As the volatile liquid exits the nozzle, it rapidly changes phase. This phase change quickly breaks up the stream into small droplets with a wide dispersion angle. The model also applies to cases where a very hot liquid is discharged.

Since the physics of effervescence is not well understood, the model must rely on rough empirical fits. The photographs of Reitz and Bracco [ 300] provide some insights. These photographs show a dense liquid core to the spray, surrounded by a wide shroud of smaller droplets.

The initial velocity of the droplets is computed from conservation of mass, assuming the exiting jet has a cross-sectional area that is $C_{\rm ct}$ times the nozzle area, where $C_{\rm ct}$ is a fixed constant, equal to 0.611 as specified in Equations  22.8-3 and 22.8-12.


 u = \frac{\dot{m}_{\rm eff}}{\rho_l C_{\rm ct} A} (22.8-37)

The maximum droplet diameter is set to the effective diameter of the exiting jet:


 d_{\rm max} = d \sqrt{C_{\rm ct}} (22.8-38)

The droplet size is then sampled from a Rosin-Rammler distribution with a spread parameter of 4.0. (See Section  22.12.1 for details on the Rosin-Rammler distribution.) The most probable droplet size depends on the angle, $\theta$, between the droplet's stochastic trajectory and the injection direction:


 d_0 = d_{\rm max} e^{- \left(\theta/\Theta_s \right)^2} (22.8-39)

The dispersion angle multiplier, $\Theta_s$, is computed from the quality, $x$, and the specified value for the dispersion constant, $C_{\rm eff}$:


$\displaystyle x$ $\textstyle =$ $\displaystyle \frac{\dot{m}_{\rm vapor}}{(\dot{m}_{\rm vapor} + \dot{m}_{\rm liquid})}$ (22.8-40)
$\displaystyle \Theta_s$ $\textstyle =$ $\displaystyle \frac{x}{C_{\rm eff}}$ (22.8-41)

This technique creates a spray with large droplets in the central core and a shroud of smaller surrounding droplets. The droplet temperature is initialized to 0.99 times the saturation temperature, such that the temperature of the droplet is close to boiling. To complete the model, the flashing vapor must also be included in the calculation. This vapor is part of the continuous phase and not part of the discrete phase model. You must create an inlet at the point of injection when you specify boundary conditions for the continuous phase. When the effervescent atomizer model is selected, you will need to specify the nozzle diameter, mass flow rate, mixture quality, saturation temperature of the volatile substance, spray half-angle and dispersion constant in addition to specifying the position and direction of the injector.


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