14-02-2013, 09:28 AM
Engineering Design Methods for Cavitation Reactors II: Hydrodynamic Cavitation
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ABSTRACT
he bubble beha¨ior and hence the pressure generated at the collapse of the ca¨ity for
hydrodynamic ca¨itation depends on the operating conditions and geometry of the mechanical
constriction generating ca¨itation. The effect of operating parameters such as
inlet pressure through the system’s orifice, initial ca¨ity size, and the indirect effect of the
hole diameter (it affects the frequency of turbulence in the ¨icinity of the orifice) on the
bubble beha¨ior was numerically studied. The bubble dynamics were simulated in two
stages considering: Rayleigh-Plesset equation up to the point of bubble wall ¨elocitys
1,500 mrs; then the compressibility of the medium using the equation of Tomita and
Shima. An empirical correlation was de¨eloped to predict the collapse pressure generated
as a function of just mentioned parameters. The trends in the magnitudes of collapse
pressure match the obser¨ed experimental trends for ca¨itation-induced reactions.
The work is an extension of the earlier analysis done for the sonochemical reactors.
Some recommendations are also suggested for the design of hydrodynamic ca¨itation
reactors based on the simulations.
Introduction
Cavitation as a source of energy input for chemical processing
is increasingly being studied because of its ability to
generate localized high temperatures and pressures hot-
spots. under nearly ambient conditions. The possibility of
successful exploitation stems from the fact that millions of
cavities grow and collapse simultaneously at different locations.
Until now, ultrasound was the main method used for
generating cavitation, and it has been extensively studied over
the past few decades. In this method, passage of ultrasound
through the cavitating medium generates cavities, promotes
their growth, and their collapse. The whole process of cavity
generation, growth, and collapse occurs over an extremely
short period of time microseconds.. In spite of extensive research,
there is hardly any chemical processing carried out on
an industrial scale using ultrasound due to the expertise required
in diverse fields, such as chemical engineering, material
science, and acoustics, for scaling up the lab scale pro-
cesses.
Mathematical Modeling of Hydrodynamic
Cavitation
Senthilkumar and Pandit 1999. have described in detail
the modeling of hydrodynamic cavitation for a venturi type of
system and also for the high-speed homogenizer. Moholkar
and Pandit 1997. have modeled the hydrodynamic cavitation
setup where flow takes place through the orifice, inserted inside
the pipe, but considered the cavitating medium to be
incompressible. The model described in the present work is
an extension of the 1997 model, only with the medium considered
compressible. The stepwise development of the turbulence
model for the hydrodynamic cavitation is described
in the following subsections.
Turbulence model
As the liquid flows through the orifice, due to reduction in
the cross-sectional area of the flowing stream, the velocity
head increases at the expense of the pressure head. During
reexpansion, the flow gets separated at the lower end of the
orifice and eddies are generated. The motion of the eddies
causes turbulence and large friction losses occur. So permanent
pressure loss is inevitable and full pressure recovery does
not take place.
A turbulence model is used to predict the instantaneous
pressure field around the traveling cavity at any downstream
location and is analogous to that proposed by Moholkar and
Pandit 1997. and Senthilkumar and Pandit 1999.. The results
of turbulence modeling and the fluctuating pressure field
can be incorporated into a bubble dynamics equation to obtain
the cavity radius history and the collapse pressures for a
cavity of a certain size, traveling with the fluid.
Results and Discussion
Collapse pressure can be defined as the magnitude of the
pressure pulse generated at the end of the collapse of the
cavity. In the present case, the collapse of the cavity is assumed
to be complete when the radius of the cavity is 0.1
times the original radius. The contribution of the adiabatic
phase to the overall pressure pulse is maximum, and hence
the simulations are terminated when RrRos0.1, and not at
the critical radius Flynn’s radius., where the collapse is completely
isothermal. The effect of the various operating parameters,
such as the inlet pressure and initial size of the
nuclei in the system, on the final collapse pressure has been
studied numerically. The size of the nuclei can be adjusted by
changing the type of cavitating medium and the system, that
is, dissolved gases, temperature, and concentration of species,
which changes the vapor pressure. The diameter of the orifice
and the percentage of free area occupied by the holes
also affect the magnitude of the collapse pressure generated.
Finally a correlation has been developed for predicting the
pressure pulse in terms of the just mentioned parameters.
Development of Correlation
The collapse pressure generated is found to be a function
of the inlet pressure, initial radius of the nuclei, the diameter
of the hole, which affects the frequency of turbulence for the
same free area, and the percentage of free area available for
the flow, which decides the liquid flow rate through the orifice.
The first three parameters resemble the operating conditions
in the system, and are quite similar to the intensity
and frequency of ultrasound and the initial radius of the nuclei
in the acoustic cavitation case.
Conclusions
The bubble dynamics and hence the pressure generated at
the collapse of the cavity is found to the dependent on the
operating parameters, such as inlet pressure through the system
of orifice, initial cavity size, and the diameter of the hole
which affects the frequency of the turbulence existing in the
reactor. The geometry of the system, that is, the percentage
of free area of the holes also affects the velocity through the
orifice, and thus affects the collapse pressure.
The selection of suitable operating inlet pressure and the
flow rate into the orifice setup. and geometric parameters
arrangement of holes on the orifice plates., and the vapor
pressure of the cavitating media is essential for carrying out
any chemical reaction using the hydrodynamic cavitation
setup. Varying these conditions can significantly alter bubble
behavior in hydrodynamic cavitation, thus achieving the required
conditions for the specific reaction. Higher values of
the inlet pressure, low initial cavity sizes, and large diameter
holes, while at the same time keeping low free area for the
flow, are found to result in high values for the collapse pressure.