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9734 Barat Ghobadian et al./ Elixir Mech. Engg. 49 (2012) 9734-9738

Available online at (Elixir International Journal) Mechanical Engineering

Elixir Mech. Engg. 49 (2012) 9734-9738

Modelling and evaluation of some effective parameters on reactor design for

optimized utilization of ultrasonic waves

Ebrahim Fayyazi, Barat Ghobadian*,Gholamhassan Najafi, Bahram Hosseinzadeh and Mehdi Montazeri Department of Mechanics of Agricultural Machinery, Tarbiat Modares University.

ARTICLE INFO Article history: Received: 6 June 2012; Received in revised form: 22 July 2012;

Accepted: 30 July 2012;


Ultrasonic, Reactor, Cavitation, Regression model, Acoustic streaming.


Ultrasonic waves are used widely in food production, industry and chemical reactions. For conducting such a reactions, it is need to have a reactor in which liquid is affected by the waves. Among the most important parameters used for reactor design, the reactor dimensions may be considered as the most important parameter that can take influence the most, from the wave cavitation. In this study, effects of ultrasonic power, horn diameter and horn height on the amount of energy absorbed by liquid in reactor were evaluated and models were further developed for estimating the absorbed energy. Statistical analysis indicated that the effects of input power, reactor diameter and reactor height were all significant on energy absorption (P<0.01). The results revealed that as the horn diameter increased from 70 to 100 mm, 9% decrease was occurred in the absorbed energy. By increasing the horn height from 30 to 70 mm, 11% decrease was observed in the energy absorption. There was an 11% increase in the energy, together with an increase in ultrasonic wave power from 100 to 300 W. It was also concluded that the second order model was most suitable to predict the amount of energy absorbed by liquid (R2=94.5%).

© 2012 Elixir All rights reserved.


When ultrasound travels through a medium, like any sound wave, it results in a series of compression and rarefaction. At sufficiently high power, the rarefaction may exceed the attractive forces between molecules in a liquid phase and, subsequently, result in the formation of cavitation bubbles. Each bubble affects the localized field experienced by neighboring bubbles.

Under such situations, the irregular field causes the cavitation bubble to become unstable and collapse, thereby releasing energy for chemical and mechanical effects. For example, in aqueous systems, at an ultrasonic frequency of 20 kHz, the collapse of each cavitation bubble acts as a localized “hotspot,” generating enough energy to increase the temperature to about 4000 K and the pressure to values higher than 1000 atm. This bubble collapse, distributed through the medium, has a variety of effects within the system depending upon the type of material involved (Kuldiloke, 2002, Nyborg 1965, Pandit and Joshi, 1983).

The most significant sonochemical (including sonoelectrochemical) effects are connected with cavitation. Sonolysis needs cavitation collapse to generate high temperatures and pressures [Schram, 1991]. Ultrasonic activation of surfaces of reactants, catalysts and/or electrodes is connected with microjets formed by cavitation. Also acoustic streaming is connected with cavitation. It is evoked by radiation pressure, and is a consequence of absorption of the ultrasonic energy. This absorption is primarily a consequence of cavitation. There is no significant sonochemical effect without cavitation (Klıim et al.,2007, Kinsler and Frey 1962).

Ultrasonic waves are used widely in liquids. For example, in order to facilitate the chemical reactions and pasteurization in food materials the ultrasonic waves are applied. In ultrasonic application, it is necessary to design a reactor in which the


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desired liquid is affected by the waves. As a result of pressure variations and cavitation occurred in liquid, heat is produced that can be used as an index for designing a sonoreactor. To obtain such a condition, effect of various factors on the mentioned factor should be studied ( Monnier et al., 1999).

In the case of acoustic cavitation, absorption of the ultrasonic wave during its propagation in the cavitating liquid is responsible for an energy gradient that induces a macroscopic liquid flow, called acoustic streaming (Bentitez, 2004).

Acoustic streaming causes the mixing effects experienced in the liquid, and therefore, it is important in the design of sonochemical reactors. An efficiency mixing is necessary, as there has been no transducer design that ensures a homogeneous distribution of the cavitation field within the reactor.

The value of mixing time can be determined by experimentation or by an empirical correlation, an example of the latter is the formula found by Vichare et al. (2001) and it’s schematic diagram shown in Fig 1:

θmix =7×10 d

 1  (1)  v2g2μ−2ρ2 

3 Z T3(T+2Z)−2d−4

6 −0.235 2 h 

θmix = mixing time, s

d = Jet length, m

Z = height of liquid in the beaker, m T = diameter of beaker, m

dh = diameter of the horn, m

vh = velocity of the horn, m/s

g = acceleration due to gravity, m/s2 μ= viscosity of liquid, Ns/m2

ρl = Density of liquid, kg/m3


© 2012 Elixir All rights reserved

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