South African Journal of Chemical Engineering 34 (2020) 57–62
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South African Journal of Chemical Engineering
journal homepage: www.elsevier.com/locate/sajce
Simulations of different power intensity inputs towards pressure, velocity &
cavitation in ultrasonic bath reactor
T
⁎
Muhammad Shafiq Mat-Shayutia,b, , Tuan Mohammad Yusoff Shah Tuan Yaa,c,
Mohamad Zaki Abdullaha, Nadiahnor Md Yusopb, Nadia Kamarrudinb,
Maung Maung Myo Thantd, Mohammad Faizal Che Daudd
a
Mechanical Engineering Department, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak, Malaysia
Faculty of Chemical Engineering, Universiti Teknologi MARA, Shah Alam 40450, Selangor, Malaysia
c
High Performance Computing Centre, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Perak, Malaysia
d
Group Research & Technology, PETRONAS, Bandar Baru Bangi 43000, Selangor, Malaysia
b
A R T I C LE I N FO
A B S T R A C T
Keywords:
Numerical analysis
User-defined function (UDF)
Ultrasonic transducer
ANSYS FLUENT
Degassing
Acoustic pressure
PIV
Various ways exist to describe power intensity in ultrasonic system, causing complications in reporting and
benchmarking. This paper attempts to compare computational fluid dynamic (CFD) simulations of ultrasonic
bath running at 60 W 40 kHz using different power intensity (also known as sound intensity) inputs viz rated
power, calorimetric power and particle velocity. Applying Schnerr and Sauer model based on Rayleigh-Plesset
equation, an abrupt streaming flow was observed during the transient period. After steady ultrasonic cycle was
reached, the simulation using rated power input recorded the highest and widest ranges of total pressure (-51.1
to 308 kPa), fluid particles velocity (7.22 to 11.5 m/s) and cavitation mass transfer (-821 to 925 kg/m3). The
sound amplitude around 200 kPa in the rated power intensity generated the greatest cavitation effects, while
particle velocity having 23 kPa sound amplitude failed to produce any cavitation bubbles. The difference lay in
the tendency of liquid molecules to vaporize (and vice versa) during sound wave oscillation. Verification with
experimental data implied the rated power feed produced the closest similarity among the three inputs.
1. Introduction
Ultrasonic technique always finds applications in chemical processes, whether in extraction, emulsification / demulsification,
cleaning, degradation of chemicals and others (Martins Strieder
et al. 2020; Mat-Shayuti et al., 2019). These processes by ultrasonic
force mainly depend on the produced cavitation and subsequent
shockwave that could release free radicals or break interfacial bond
between phases (Abramov et al., 2009; Mason et al., 2004). Numerical
simulation could provide insight into deeper comprehension of sonication effect, necessary for ultrasonic system improvement. It cuts resources needed for experiment by virtually manipulating parameters
and predicting outcomes. Considerable amount of studies was reported
with regards to simulating ultrasonic field using computational fluid
dynamic (CFD). Some approaches required massive computational resources to get down to the lowest scale and predict results accurate to a
single bubble dynamic (Merouani et al., 2013; Osterman et al., 2009).
On the opposite end, others focused on simplicity for quick solution by
applying generic model for specific ultrasonic system. For instance,
⁎
Trujill and Knoerzer (2009) utilized a CFD model founded by J.
Lighthill for prediction of acoustic streaming in ultrasonic horn system,
while Tiong et al. (2015) performed acoustic pressure simulation for
VialTweeter based on Helmholtz equation. Regardless of approaches
taken, one must use standardized ultrasonic parameters to ensure accuracy of computational results.
This study revolved around an ultrasonic bath reactor where a
piezoelectric transducer was mounted to the reactor's bottom with
surface ratio of the transducer to the reactor's bottom was almost 1:1.
The modeling of sound field was taken directly from the acoustic theory
(Cai et al., 2009) and previously proven to work with ultrasonic bath
system (Abolhasani et al., 2012). The state of sound pressure or also
known as acoustic pressure at inlet or ultrasonic source, Pinlet (Pa), with
respect to time, t (s), and space coordinate, z (m), is given as
Pinlet = Pampcos[ω (t + z / C ]
(1)
where Pamp is sound pressure amplitude (Pa) with angular frequency, ω
(rad/s), and sound speed in water, C (m/s). z is equal to 0 when inlet is
treated as datum. Theoretical Pamp which is the maximum sound
Corresponding author.
E-mail address: mshafiq5779@uitm.edu.my (M.S. Mat-Shayuti).
https://doi.org/10.1016/j.sajce.2020.06.002
Received 13 May 2020; Received in revised form 2 June 2020; Accepted 11 June 2020
1026-9185/ © 2020 The Author(s). Published by Elsevier B.V. on behalf of Institution of Chemical Engineers. This is an open access article under the CC
BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
South African Journal of Chemical Engineering 34 (2020) 57–62
M.S. Mat-Shayuti, et al.
2.2. Meshing
pressure is calculated by
Pamp =
2IρC
(2)
A total of 16,000 meshes and 16,281 nodes were generated,
achieving minimum orthogonal quality of 9.98865e−01. The maximum
ortho skew and maximum aspect ratio were 1.13483e−3 and 1.45932,
respectively.
where ρ denotes density (kg/m ) of medium where sound is traveling.
Power intensity or sound intensity, I (W/m2), however, can be computed by various approaches. Despite having the same unit, they have
different definition and their magnitudes can differ significantly. The
common practice is to divide ultrasonic rated power, Prated (W) or calorimetric power, Pcal (W) by irradiation area, A (m2) which gives
3
P
or Pcal
I = rated
A
2.3. Physics setup and numerical method
In the pressure-based solver of transient mode, mixture model of
multiphase fluids was switched on as the problem involved water liquid
and vapor, with no slip velocity setting. Energy equation was required
to enable cavitation mass transfer between water liquid and vapor. For
the turbulence model, standard k-epsilon model and standard wall
function were set.
The general vapor transport equation that governs cavitation mass
transfer is described as
(3)
where Prated is quoted from manufacturer and Pcal is standardized by the
International Electrotechnical Commission Standard to be
Pcal =
dT
CP M
dt
(4)
→
∂
(αρv ) + ∇ . (αρv Vv ) = R e − R c
(7)
∂t
→
where α, ρ, and Vv are volume fraction, density, and phase velocity,
respectively, while v refers to the vapor phase. The mass transfer source
term for vapor bubbles growth is Re and for vapor bubbles collapse is
Rc. The bubbles dynamic equation which is derived from RayleighPlesset equation is given by
Temperature variation rate is expressed as dT (K/s), liquid medium's
dt
specific heat capacity as CP (J/kg K), and its mass as M (kg). On the
other hand, particles velocity, V (m/s), can be used to calculate I as
(Gao et al., 2015)
I=
Pa2
ρV
(5)
or
I = Pa V
RB
(6)
D 2 RB
3 R 2
P − P⎞
4vl
2S
+ ⎛ B ⎞ = ⎜⎛ B
RB −
⎟ −
Dt 2
2 ⎝ Dt ⎠
RB
RB
⎝ ρl ⎠
(8)
with ℜB is bubble radius, PB is bubble surface pressure and P is far-field
pressure. Any terms with l in the equation correspond to liquid phase.
Schnerr and Sauer cavitation model was chosen in this study because of
its versatility. It can be used with all turbulence schemes and most of
numerical solvers offered in ANSYS FLUENT, while at the same time has
the robustness to deal with compressible fluid and non-conformal mesh
interface. Further setting saw vaporization pressure set at 3540 Pa and
bubble number density of 1e+13. The solution method utilized SIMPLE
scheme and PRESTO mode for pressure in spatial discretization. The
remaining numerical method followed the recommendations in ANSYS
FLUENT manual.
In this work, ultrasonic setting at 60 W 40 kHz was selected due to
accessibility to experimental data and for being deemed as the middle
frequency between low (20 kHz) and high (60 kHz) frequencies in
kilohertz-range ultrasonic bath system. To simulate ultrasonic irradiation at the inlet pressure boundary, a user-defined function (UDF) was
coded as per Fig. 2. The time step used was one-sixteenth of the 40 kHz
ultrasonic period to ensure the simulation capture all the ultrasonic
effects and avoid floating error. Iteration was fixed at 10 times per time
step.
where Pa is the acoustic pressure (Pa). It can be seen that there are
multiple approaches to assume the value of I, each is dimensionally
correct and holds the premise to simulate the ultrasonic condition in
ultrasonic system. Therefore, this investigation tried to explore the ultrasonic effects differences in ultrasonic bath reactor when different I
values were used in simulation and comment on their resemblance with
experimental result.
2. Methodology
2.1. Geometry modeling & boundary condition
The cylindrical bath reactor of 8 cm diameter x 20 cm tall as demonstrated in Fig. 1 was modelled in 2D configuration. The bottom
wall as the ultrasonic source was assigned pressure inlet, the water-air
interface at the top was allotted as pressure outlet, while the cylinder
wall was treated as normal wall condition.
2.4. Verification and validation
Some parameters of the simulation were validated in separate experiments for the ultrasonic bath at 60 W 40 kHz setting. Sonic Meter
SM 1000 was probed into the reactor to map the acoustic pressure
distribution, while particle image velocimetry (PIV) system from
Dantec Dynamics was operated to measure the fluid particles velocity,
V.
3. Result & discussion
3.1. Transient period
A transient period showcasing dynamic evolution of total pressure
in Fig. 3 was observed when rated power was used as input. A
streaming band of low pressure (consisted of bubbles) could be
Fig. 1. The ultrasonic cylindrical bath reactor showing boundary conditions.
58
South African Journal of Chemical Engineering 34 (2020) 57–62
#include "udf.h"
DEFINE_PROFILE(inlet_profile,thread,position)
{ face_t f;
real t=CURRENT_TIME;
begin_f_loop(f,thread)
{
F_PROFILE(f,thread,position)=P amp*cos(ω*(t+(z/C));
}
end_f_loop(f,thread)
}
/replace the values of Pamp, ω, z and C accordingly.
Inlet pressure, Pinlet (kPa)
M.S. Mat-Shayuti, et al.
Rated power
Calorimetric power
Acoustic Intensity
300
200
100
0
1
-100
-200
Time, t (s)
Fig. 2. UDF code for pressure inlet cycle modeling ultrasonic pattern at 60 W 40 kHz and its graphical representation.
other hand showed very little difference between transient and steady
periods.
observed moving upwards from the bottom. The streaming stopped as it
reached near the water surface and its total pressure enlarged. Now the
reactor was divided into 2 regions, above and below the streaming
band. The pressure in the former now amplified while the latter declined. The bottom region area gradually retracted and at the same time
plunging in total pressure. Simultaneously, the interface between the
top and bottom regions exhibited localized high-pressure points as indicated by the red dots, which eventually died down as the bottom
region totally withdrew. In an experiment, this initial fluid stream from
the ultrasonic source to the water-air interface was immediately seen as
the ultrasonic generator switched on. It also could represent the degassing process of the fluid. Beyond this milestone (0.01745 s), the
pressure oscillation in the reactor corresponded accordingly to the ultrasonic irradiation given by the ultrasonic source and is termed as
steady period. Calorimetric power and particle velocity inputs on the
3.2. Steady period
Fig. 4 illustrates the total pressure in the ultrasonic reactor during
pressure hike and descent, proving the expediency of the written UDF
to integrate well with all the physics setup and numerical schemes in
the solution. The interaction between the set oscillation and fluid
properties can be seen to influence the pressure and other ultrasonic
effects across the reactor. Fig. 5 portrays the corresponding individual
plots for total pressure, velocity magnitude, cavitation and liquid phase
fraction. Those of rated power input show the maximum values with
the largest ranges, followed by calorimetric power and particle velocity.
The finding could be attributed to the declining power intensity as rated
Fig. 3. Total pressure transition during transient period from 0 to 0.01745 s (from i-viii) when rated power input was used.
59
South African Journal of Chemical Engineering 34 (2020) 57–62
M.S. Mat-Shayuti, et al.
Fig. 4. Increasing and decreasing pressure cycle during steady period. Notice the variation in total pressure across spatial and temporal dimensions of the ultrasonic
reactor which influenced the ultrasonic cavitation.
power was replaced with calorimetric power and calorimetric power
substituted by particle velocity. For cavitation to occur, water needs to
boil locally and produces vapor bubbles in low surrounding pressure.
Cavitation then is recorded as mass transfer (kg/m3) from liquid to
vapor phase. When these bubbles are subjected to high-pressure ambience during ultrasonic ascension, they will implode. At this instance,
the cavitation bubbles undergo phase change again from vapor to liquid, known as condensation. The highest manifestation of cavitation
found in the rated power input was echoed by the largest vapor volume
fraction, whereas the input using particle velocity failed to generate
bubbles although at one point generated −1.63 × 104 Pa total pressure. Cavitation bubble formation was observed in the experimental
study of 60 W 40 kHz ultrasonic bath reactor, thus particle velocity
input is rejected.
Fig. 6 portrays the comparison between experimental acoustic
pressure, Pa (Pa) and simulated total pressure dissipations within the
reactor. The trend of attenuation was fitted according to the power law,
where the closest proximity to the experimental value was shown by the
rated power input, trailed by calorimetric power and particle velocity.
up 5–50 W 490 kHz ultrasonic bath experiment and detected up to
160 kPa sound pressure using ONDA HNR-1000 probe. Then
Csoka et al. (2011) simulated 3.3 L ultrasonic bath at 220 W 224 kHz
and recorded maximum 56 MPa pressure. Later Koch (2016) used selfmade needle hydrophones in ultrasonic bath at 5–30 W 45 kHz to get
50–500 kPa. Interestingly, none of these works complemented their
findings with numerical study or vice versa, hinting the problem with
sound pressure prediction. Correction factor for ultrasonic model could
be introduced via extensive experiment to ease the disagreement between the measured sound pressure and theoretical total pressure.
In the meanwhile, the fluid particle velocity was underestimated
due to several reasons. There is no high-speed camera capable of capturing each cycle of 40 kHz ultrasonic oscillation, thus the velocity
recorded was just an averaged interpretation of the particle velocity,
which was made even lower by the interference of standing wave regions. As with any engineering application, the use of statistical
methods for measurement system and optimization may be performed
to improve result accuracy and performance of the ultrasonic system
(Ab Hamid et al. 2020; Mat-Shayuti and Adzhar 2017).
3.3. Error analysis
4. Conclusion
There is slight difference between the pressures compared in Fig. 6
which caused 41% discrepancy. The sound/acoustic pressure is the
local pressure deviation from surrounding caused by sound wave,
measured as sound force on a surface area. While Pinlet was entirely
sound pressure, the simulated total pressure covered other pressure
components viz static, dynamic and hydrostatic pressures. The study of
acoustic pressure in ultrasonic bath is limited. Kojima et al. (2010) set
Lack of standardization for certain ultrasonic parameters’ equations
are causing confusion over the computation. Evaluation of simulations
comparing three different inputs for power intensity in a customized
ultrasonic bath showed that the rated power gave the best representation of the actual system as compared to the calorimetric power and
particle velocity. The simulated effects were superior for the rated
power input in all criteria namely total pressure, velocity magnitude
60
South African Journal of Chemical Engineering 34 (2020) 57–62
M.S. Mat-Shayuti, et al.
16
Total pressure (kPa)
300
Velocity magnitude (m/s)
308
200
100
64.7
20.1
-16.3
0
-51.1
-100
Rated power
-58.8
Calorimetric power
12
11.5
10.1
8
5.17
3.69
4
0
Rated power
Particle velocity
Calorimetric
power
Water liquid
1200
Volume fraction
400
132
0
-400
0
-455
-800
Particle velocity
Water vapour
1
925
800
Cavitation (kg/m 3)
7.81
7.22
0.995
0.99
0.985
0.98
-821
0.975
-1200
Rated power
Calorimetric power
Rated power
Particle velocity
Calorimetric
power
Particle velocity
Fig. 5. Various ranges of ultrasonic effects within the reactor.
600
500
Pressure (kPa)
Declaration of Competing Interests
Experimental acoustic pressure
Simulated total pressure from rated power
Simulated total pressure from calorimetric power
Simulated total pressure from particle velocity
400
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
300
Acknowledgment
200
This work was supported by the Ministry of Education, Malaysia,
through Fundamental Research Grant Scheme [600-IRMI/FRGS 5/3
(192/2019)]. Special thanks also to the Group Research & Technology
PETRONAS for the supports rendered.
100
0
0
-100
2
4
6
8
10
12
14
16
18
20
Distance from Ultrasonic Source (cm)
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CRediT authorship contribution statement
Muhammad Shafiq Mat-Shayuti: Writing - original draft,
Methodology, Software. Tuan Mohammad Yusoff Shah Tuan Ya:
Supervision. Mohamad Zaki Abdullah: Supervision. Nadiahnor Md
Yusop: Validation. Nadia Kamarrudin: Validation. Maung Maung
Myo Thant: Conceptualization, Resources. Mohammad Faizal Che
Daud: Conceptualization, Resources.
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