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The effect of geometrical parameters on the characteristics of ultrasonic processing for metal matrix nanocomposites (MMNCs)
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Technical Paper
The effect of geometrical parameters on the characteristics of ultrasonic processing for metal matrix nanocomposites (MMNCs) Pavan Pasumarthi, Saheem Absar, Hongseok Choi ∗ Department of Mechanical Engineering, Clemson University, Clemson, SC, United States
a r t i c l e
i n f o
Article history: Received 16 December 2015 Received in revised form 29 March 2016 Available online xxx Keywords: Metal matrix nanocomposites Ultrasonic processing Dimensional effect Acoustic cavitation Helmholtz equation
a b s t r a c t Metal matrix nanocomposites (MMNCs) can offer significant improvement of properties such as higher specific strength, specific modulus, controlled thermal expansion and higher corrosion resistance, compared to the base metallic materials. However, agglomeration or clustering of nanomaterials makes it very difficult to disperse them in the metal matrix. Non-linear effects of ultrasonic processing, such as acoustic cavitation and acoustic streaming, help in the dispersion and distribution of the nanomaterials. Non-linearity of the ultrasonic processing makes it very hard to measure or characterize the process experimentally. There is very limited knowledge about the interactions between the geometrical parameters of the ultrasonic processing and the extent of cavitation achieved. Numerical modeling offers powerful tools to overcome the experimental difficulties involved. In this study, a non-linear numerical model was developed to resolve the acoustic pressure field, and the cavitation zone size was quantified from the numerical modeling results. The model was then used to study the effect of geometry on the cavitation zone size. Analysis of variance (ANOVA) was used to identify the significant parameters. A parametric analysis involving these parameters was subsequently performed. A configuration of geometrical parameters offering the highest cavitation zone size was determined. It was found out that a probe immersion depth of 25.4 mm produced a maximum cavitation zone in the ultrasonic processing cell with a diameter of 35.9 mm for processing 57 ml of molten Al alloy. An experimental validation has been accomplished by ultrasonically processing an aluminum alloy with carbon nanofibers and silicon carbide microparticles. With selected parameters the area of micro pores in the MMNC was significantly decreased by 50% and a deviation of the hardness was also decreased by 46% due to further dispersion and distribution of the carbon nanofibers. © 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Ultrasound with a frequency above 20 kHz can be classified into two groups: power ultrasound and diagnostic ultrasound based on its frequency range [1]. For material processing applications such as degassing, mixing, synthesis, or liquid metal treatment, the power ultrasound (20 kHz to 2 MHz) is more suitable than the diagnostic one [1] due to its higher amplitude and non-linear effects like acoustic cavitation and acoustic streaming. In the current study, ultrasound with the frequency of 20 kHz was used to disperse and distribute nanomaterials to manufacture metal matrix nanocomposites (MMNCs) which are advanced materials incorporated with nanomaterials as reinforcements [2]. MMNCs have shown enormous potential especially in structural applications, by offering
∗ Corresponding author. E-mail addresses: [email protected] (P. Pasumarthi), [email protected] (S. Absar), [email protected] (H. Choi).
excellent strength to weight ratio, along with mechanical properties such as ductility, fatigue, hardness, etc., showing significant improved properties compared to the base materials [2]. Currently, the manufacturing technologies of MMNCs can be classified into solid- and liquid-base processes [2]. Among those technologies, the liquid-base process is the most efficient and cost-effective method. However, it is very difficult to uniformly disperse nanomaterials in molten metal using conventional stirring methods because the shear stresses generated are not enough to break the bonding strength of the nanomaterials caused by mutually attractive van der Waals forces [2–4]. Ultrasonic processing utilizes non-linear effects such as acoustic cavitation and acoustic streaming, to disperse and distribute the nanomaterials in molten metals. This process shows promising results with relatively uniform dispersion and distribution of the nanomaterials in various metal matrices [5–8]. The acoustic cavitation can generate enough stress to break the agglomeration of the nanomaterials and the acoustic streaming can produce enough flow to disperse them in the molten metal. The acoustic cavitation is a generation of gas bubbles that occur
http://dx.doi.org/10.1016/j.jmapro.2016.06.019 1526-6125/© 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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during the rarefaction cycles of the acoustic pressure wave during ultrasonic processing. Under the subsequent ultrasound field, the cavities pulsate until reaching a critical radius after which they implode. The trapped air pockets in the nanomaterial clusters also act as the cavitation seed nuclei, from which cavitation bubbles originate. During the implosion the released shock waves break apart the clusters, leaving nanomaterials dispersed throughout the liquid metal. The dispersed nanomaterials are distributed homogenously by the acoustic streaming flow. It should be noted that the collapse of cavitation bubbles results in the generation of extremely high temperatures and pressures [9], and a micro-jet is also reported to be observed [10]. But, these implosions are very short lived (in the order of pico-seconds) and extremely localized. Acoustic streaming is a non-linear consequence of the attenuation of ultrasonic wave during its propagation. The ultrasonic wave attenuates very rapidly in a short space interval [11]. The attenuation of the wave generates a pressure difference in the liquid that generates flow. A system for the ultrasonic processing of liquids consists of two principal parts: an excitation source and a liquid load. The excitation source produces an ultrasonic energy, which is then delivered to the liquid through an ultrasonic probe. The liquid is contained in a vessel that is termed an ‘ultrasonic processing cell’. The ultrasonic processing cell can be made of different materials depending on the applications. There are several factors that affect ultrasonic processing of liquids. Appropriate design and configuration of the ultrasonic processing equipment is very critical for the effectiveness of ultrasonic processing. In current practice of the ultrasonic processing of liquids, the processing parameters are mainly selected by heuristic arguments or based on the experience of operators. The experimental knowledge is extremely limited and highly subjective because of the process dependence on the physical parameters such as the dissolved gas content. Kumar et al. [12] quantified the uniformity of cavitation field by introducing a new quantity called the degree of uniformity. In their work, hydrophones were used to make the measurements. However, the hydrophones inside the liquid can have microscopic pockets of air trapped on their surfaces and they will interfere with the acoustic cavitation process. Lee et al. [13] took high speed photographs of the bubble structures, but they were unable to extract holistic information that can explain the mechanism of the acoustic cavitation. Gogate et al. [14] calculated the efficiency of the cavitation reactors by using a model reaction. The repeatability of the process is poor because the purity of the liquid used is not considered. On the other hand, various numerical models of the acoustic pressure field inside the sonochemical reactor have been intensively developed. Most of them simulate the acoustic pressure field in the sonochemical reactor filled with water. They are based on the linearization of the Euler equations [15], which generate the Helmholtz equation for the ultrasonic wave propagation. The linear Helmholtz equation is very robust and easily solvable using finite element method (FEM). Recently, attempts have been made to simulate cavitation formation and implosion inside the reactor [16–18]. It should be noted that there is an uncertainty involved in the models because of the time variation and spatial scales in the cavitation process. However, several authors have studied the modeling and prediction of the cavitation distribution inside the sonochemical reactor [19–21]. They are based on the linearization of Caflisch equations, which is a widely accepted notion that relates the cavitation bubble fraction at any point to the corresponding acoustic pressure [22]. Based on the previous research on the pressure field inside the sonochemical reactor [11,23,24], in this study, the cavitation formation and implosion is characterized using the numerical model which was developed to resolve the acoustic pressure field inside the ultrasonic processing cell. The
numerical model is then used to investigate the dimensional effect of different geometric configurations of the ultrasonic processing cell and the position of the ultrasonic probe on acoustic cavitation. Finally, an experimental validation is conducted to verify the developed numerical model. 2. Numerical modeling The following wave equation [11] describes the acoustic pressure variation in space and time, as given in Eq. (1):
∇
1
∇P −
2
1 ∂ P = 0, c 2 ∂t 2
(1)
where P is the acoustic pressure, is the density, c is the speed of sound, and t is the time. Since most ultrasound sources emit sinusoidal waves, assuming the pressure wave is harmonic in nature is quite reasonable, P(r, t) = p(r) · eiωt ,
(2)
where ω is the angular frequency of the ultrasonic wave and is given by ω = 2f, where f is the frequency in Hz, and r describes the position in (x, y, z) coordinates. Substituting Eq. (2) in Eq. (1), the linear homogenous wave equation can be obtained, which is only dependent on the spatial variable r:
∇
1
∇P −
2
ω2 ∂ P =0 c 2 ∂t 2
∇ 2 P + k2 P = 0
(3) (4)
Eq. (4) is known as the Helmholtz equation with acoustic pressure P, wave number k given by Eq. (5): k=
ω c
(5)
Although the above linear model describes the geometric attenuation due to multiple reflections and wave dispersion, it ignores the attenuation due to the liquid properties. To describe the damping properties of a medium, the complex sound speed, cc and the complex density, c of the medium are defined as follows [15]:
cc = c
c =
4
1 + iω
c 2 cc2
3
+ b
0.5
c 2
,
(6)
(7)
where is the dynamic viscosity and b is the bulk viscosity of the medium. 2.1. Modeling geometry An axisymmetric geometric section of the ultrasonic processing cell and the ultrasonic probe was modeled, which is shown in Fig. 1(a). The ultrasonic probe is immersed into the liquid up to a height d. The cell geometry is given by diameter D and height H. The probe diameter is Dp . The parameters for the modelling were obtained from experimental results published by Sutkar et al. [25], where they used a hydrophone to measure the acoustic pressure values along the axis of the ultrasonic processing cell. 2.2. Boundary conditions The ultrasound waves propagate differently in different media. Impedance of the medium is the material property that dictates the
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Fig. 1. (a) Axisymmetric geometrical model and (b) chosen boundary conditions, including unstructured mesh.
propagation characteristics of the ultrasound wave. Impedance of the medium is given by Eq. (8): Z = × c,
(8)
where is the density of the medium and c is the speed of sound in the medium. Several researchers have attempted to resolve the numerical models using either infinitely hard or partially reflecting boundaries [26]. However, the hard and soft boundaries are idealized cases. In practice, almost all the boundaries are considered as ‘discontinuous boundaries’. The discontinuity is in the impedance. As the sound wave propagates across the boundary between two different media, it experiences a change in the impedance of the medium. This affects the propagation characteristics of the ultrasound wave. One way to quantify the impedance mismatch is to calculate the reflection coefficient at the interface given by the following expression [23], given by Eq. (9): Rce =
Z − Z 2 2 1 Z2 + Z1
,
(9)
where Z1 and Z2 are the impedances of the two media. The pressure field that is generated inside the ultrasonic processing cell is the resultant of interactions between the reflected waves from the boundaries and the incident ultrasound wave. The chosen boundary conditions for the model are shown in Fig. 1(b). The side walls of the ultrasonic probe that are immersed in water are modeled as rigid walls. Mathematically it can be represented by Eq. (10):
∂p = 0, ∂n
(10)
where n is the plane normal to the boundary. The boundaries between interfaces are given using the impedance boundary condition. There are two interfaces in the current reactor: the interface between water and glass, and the interface between water and air. The tip surface of the ultrasonic probe is modeled as a pressure boundary condition [27]. The pressure amplitude at the probe surface can be given by Eq. (11): Pa =
2Ic,
(11)
where Pa is the pressure amplitude of the ultrasonic probe, is the density of water and c is the speed of sound in water. I is the intensity of the power input into the medium, given by Eq. (12): I = I0 × ,
(12)
where is the factor of conversion of the ultrasonic probe assumed to be around 0.85 [28] and I0 is the intensity of power input into the ultrasonic probe. 2.3. Discretization In finite element modelling of the acoustic pressure field, the node length should satisfy the following condition [27], given by Eq. (13):
h
l
1,
(13)
where hl is the node length, which is the size of the longest side of the triangular mesh element and is the wavelength of the sound wave. In order to conserve computational resources, an unstructured mesh was utilized. The region closer to the probe tip surface has much finer meshes than ones in other areas of the domain, as shown in Fig. 1(b). The longest node length in this case is 0.0128 cm, which satisfies the condition specified by Eq. (13). The unstructured mesh was selected because of the fact that the cavitation zone is often concentrated in the region immediately below the probe tip surface [1]. The finer discretization around the probe tip surface was applied to a round area with a diameter of about /10 [7]. 3. Numerical results The finite element model for calculating the acoustic pressure field inside the ultrasonic processing cell was solved using the commercial FEM package, COMSOL Multiphysics 5.1. 3.1. Acoustic pressure field In order to study the effect of the boundary conditions on the acoustic pressure field, an analysis with two different boundary condition configurations was performed. In the first configuration, the side walls were considered to be infinitely hard and the top boundary was considered as a soft boundary. In the second configuration, both the side walls and the top wall were considered to be partially reflecting. There is an impedance mismatch between the media that is being considered. The surface of the ultrasonic probe remained as infinitely hard in both cases. The impedance mismatch between water and the titanium ultrasonic probe is excessively high, hence majority of the ultrasonic waves reflect back, and very little passes through the interface.
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4 Table 1 Parameters for the numerical model. Parameter
Value
D, cm DP , cm H, cm d, cm t, cm Frequency, Hz P, W
13.5 2 17 2 0.3 20,000 36
It was observed that the boundary conditions have an impact on the resultant acoustic pressure field. The ultrasound wave is partially transmitted through the boundary and the rest is reflected back into the ultrasonic processing cell. Since the glass wall has higher acoustic impedance compared to water, the majority of the ultrasound wave is reflected back but a portion of them is transmitted through the glass wall. The transmitted waves travel to reach the next boundary. At the interface between glass and air, the ultrasonic waves once again undergo partial reflection. While the ultrasonic waves leave the glass wall (higher acoustic impedance) into the air (lower acoustic impedance), the majority of the ultrasound waves are transmitted through the interface while a minor portion is reflected back. The reflected waves inside the glass wall undergo multiple reflections, and then some of them return into the water and start interacting with the existing ultrasound waves. The final boundary conditions selected for this model are shown in Fig. 1(b). The results clearly showed that the area of higher acoustic pressure magnitude inside the ultrasonic processing cell is relatively larger than that the cases considering either infinitely hard or partially reflecting walls as boundary conditions. 3.2. Validation The numerical results from the non-linear acoustic pressure field model was validated by comparing to those reported by Sutkar et al. [25], consisting of experimental measurements of the acoustic pressure along the axis of a sonochemical reactor, measured using hydrophones. As explained in the previous section, an FEM model for calculating the acoustic pressure field inside the ultrasonic processing cell has been developed. The geometric and operational parameters used are listed in Table 1. The ultrasonic processing cell was made of borosilicate glass, a standard thickness of 0.3 cm, with a diameter of 13.5 cm and the liquid level was 17 cm. The probe was positioned at 2 cm below the water surface. An ultrasonic source of 20 kHz and a power of 36 W were used. The model was solved using the commercial FEM package, COMSOL Multiphysics 5.1 (COMSOL, USA). Meshing was performed based on the previous discussion. The additional glass thickness is also meshed similar to the liquid domain adjacent to it. The mesh is shown in Fig. 1(b). The wall thickness of 0.3 cm is very small compared to the wavelength of the ultrasonic wave, so a relatively coarser mesh used in the wall thickness would be appropriate to capture the acoustic pressure wave. Fig. 2(a) clearly shows that the pressure along the axis from the simulation result is reasonably similar to the reported experimental measurements. The resultant acoustic pressure field obtained from the numerical model is shown in Fig. 2(b). The experimental measurements of the acoustic pressure along the axis of a sonochemical reactor were conducted using hydrophones [25]. The measurements start at a distance of 1 cm from the probe tip surface and continue at 14 different points with the last measurement taken at 14 cm. The solid line represents the experimental measurements, and the dashed line shows the numerical calculations. An error
analysis revealed that the mean error is about 33%, with a maximum error of 78% at a point 2 cm away from the probe tip surface and a minimum error of 5.8% at a point 4.5 cm away from the probe tip surface. It can be observed that the difference between the numerical results and the experimental measurements is larger when the measurement is close to the probe tip surface and the bottom surface of the ultrasonic processing cell. This would be caused by the fact that when the hydrophone is close to the probe tip surface or the bottom surface of the ultrasonic processing cell, the interference caused by the existence of the hydrophones would be constructive. The difference would be proportional to the distances between the hydrophone and the probe tip surface and the ultrasonic processing cell bottom surface. 3.3. Characterization of cavitation zone While the acoustic pressure field is a useful result, there is no directly available information about the cavitation formation and implosion inside the ultrasonic processing cell. It is known that cavitation only takes place at locations where the acoustic pressure is above the threshold pressure. In this study, the cavitation area is used to quantify the cavitation formation and implosion inside the ultrasonic processing cell. Cavitation is the generation of gas filled cavities inside a fluid. There are two types of acoustic cavitation that are reported [29]: • Stable cavitation: involves the oscillation of bubbles in the ultrasonic field whose size is close to their equilibrium bubble sizes. These oscillations typically last several acoustic cycles and are generally larger in size than transient bubbles. • Transient cavitation: involves bubbles of several different sizes oscillating volumetrically (expanding and contracting) in the ultrasonic field. The oscillations continue until the cavities reach a critical radius upon which they implode. The implosion events generate shockwaves and micro-jets, which are accompanied by tremendous amount of pressure (few hundred atmospheres) and high temperatures (few thousand K). These extreme conditions occur in highly localized areas and are retained for extremely short time (ps). Cavitation occurs during the rarefaction cycle of the ultrasound pressure wave. Theoretically, when the negative pressure exceeds the threshold pressure, voids are formed in the liquid. The dissolved gas inside the liquid diffuses into the void forming a gas cavity [30]. The transient cavitation threshold value in several liquids has been investigated by several authors over the years. However, in practice, every liquid has dissolved gases in the form of micron sized cavities which act as the seed nucleus for the cavitation under the sound field [30]. Blake developed an equation for calculating the cavitation threshold by incorporating the equilibrium bubble radius into the term [30] given by Eq. (14). The ‘equilibrium bubble radius’ is the radius at which a gas bubble is stable in a given liquid in the absence of an external sound field. This is in fact the radius of the seed nuclei that act as the cavitation spots [30,31]. 4
× Pb = P0 − Pv + 3
2 × 3 P0 +
2
R0
− Pv × R0 3
(14)
where Po is the ambient pressure which is 101,325.23 Pa, Pb is the cavitation threshold pressure, Pv is the vapor pressure of water which is 3,173.032 Pa, is the surface tension of water, 73.0 mN/m, and Ro is the equilibrium radius of the cavitation bubbles, 0.08 m [30]. All the properties of water were taken at 298 K. The threshold pressure for cavitation was found to be 0.8 MPa. Using this value, the regions inside the ultrasonic processing cell where the acoustic
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Fig. 2. (a) Validation of numerical model with experimental results from [25], (b) Resolved acoustic pressure field.
the height of the ultrasonic processing cell, rather the height of the liquid inside the ultrasonic processing cell. When the ultrasonic probe is immersed into the liquid, there is a rise in the liquid level and it changes the value of H. Fig. 1(a) illustrates all geometrical parameters and determination of each parameter is given below: • Real height, H: This is the final height of the liquid level when the ultrasonic probe is immersed into the liquid, including the height rise (H), given by Eq. (15): H = H + H
(15)
• Nominal height, H : This is the height of the liquid level before the ultrasonic probe is inserted into the liquid, given by Eq. (16): H = Fig. 3. Typical plot for the cavitation zone measurement.
pressure exceeds the threshold were identified, as shown in Fig. 3. The dark region is the cavitation zone in which the cavitation will occur, and the white regions have little probability of cavitation formation. It should be noted that it is very challenging to exactly anticipate the location of cavitation bubble generation. The cavitation zone location is the most exhaustive information which can be obtained from the acoustic pressure field. In order to compare the cavitation zones in different geometrical configurations of the ultrasonic processing cell and the position of the ultrasonic probe, two new mathematical quantities were defined in this study (shown in Fig. 3): • Equivalent area (Aeq ): The area of a circle which has same area as of the cavitation zone in a particular configuration. • Equivalent diameter (Deq ): It is the diameter of the circle whose area is given by equivalent area (Aeq ). 4. Design of experiments for geometrical parameters There are various geometrical parameters involved in ultrasonic processing. Cell dimensions such as the ultrasonic processing cell diameter (D), height (H) and volume (V) and the ultrasonic probe position - given by its immersion depth (d) and diameter (Dp ) are important. The probe diameter (Dp ) was kept as a constant value of 1.27 cm. It is to be noted that the height (H) does not represent
4×V × D2
(16)
• Rise height, H: This is the rise in the liquid level after the ultrasonic probe is immersed into the liquid, given by Eq. (17): H =
0.5 × Dp3 D2
(17)
Two new geometrical parameters defined as diameter ratio (D/DP ) and immersion depth ratio (d/DP ) were introduced in this study. The three parameters – diameter ratio, immersion depth ratio and liquid volume are of interest to investigate the effect of the geometrical parameters on ultrasonic processing. 4.1. ANOVA In order to find the optimal geometric configuration and reduce the number of simulations in the parametric analysis, the statistical technique of analysis of variance (ANOVA) was employed. The three geometrical parameters – diameter ratio, immersion depth ratio and volume were considered as the three factors whereas the equivalent diameter (Deq ) was considered to be the response variable. The goal of the study was to find out the factors that are more significant in determining the response variable, Deq. For a full factorial experiment with 3 factors and 3 levels, a total of 27 runs were performed. Each factor has a high level, a low level and a mid-point. Selection of the high and low levels for factors is a very important aspect of ANOVA. For the diameter ratio, a lower level of 1.25 was selected considering the physical feasibility of the
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6 Table 2 Factors and 3 levels selected for DOE.
4.2. Parametric analysis
Factor
Low level (−1)
Mid-point (0)
High level (+1)
(D/DP ) (d/DP ) Volume (cc)
1.25 0.25 50
2.25 1.625 125
3.0 3.0 200
set-up. A (D/DP ) value of 1.25 gives an ultrasonic processing cell diameter of 1.5875 cm for an ultrasonic probe with a diameter of 1.27 cm. This leaves a gap of 0.15875 cm between the sides of the probe and the inside walls of the ultrasonic processing cell. A gap less than 0.15875 would not be practical for an experimental setup. The high level was selected to be 3.0 from the literature [32]. It has been reported that the radial variation of acoustic pressure field is very pronounced when the distance between the probe center and the inside walls is less than 1.5 times the probe diameter. Above this point there is a significant decrease in ultrasonic power intensity. For the immersion depth ratio, the lower level of 0.25 was selected. This gives an immersion depth of 0.3175 cm. Although it is only a quarter of the probe diameter, the ultrasonic probe would still transmit ultrasound waves into the liquid. With a shallower immersion depth below this point, however, the coupling of the ultrasonic waves with the liquid is expected to be very poor. A higher level of 3.0 was selected for the (d/DP ) value based on the design limit for the immersion depth of the ultrasonic probe in a sonochemical reactor [33]. The lower and the higher volume limits were selected to be 50 cc and 200 cc, respectively. When the volume is 50 cc with (D/DP ) of 3.0, it gives the real height of 4.445 cm, which allows a gap of only 0.635 cm between the tip surface of the ultrasonic probe and the bottom surface of the ultrasonic processing cell for the immersion depth ratio of 3.0. Similarly the higher level of volume was selected to be 200 cc. The selected factors and levels for this study are shown in Table 2. A total of 27 different geometrical configurations were solved for the response variable, Deq . A plot of standardized effects based on the ANOVA results is shown in Fig. 4. Significance is determined based on the distance of each point from the normal line. The farther a point is from the line, the more it influences the response variable. It can be clearly observed that two factors - the diameter ratio and immersion depth ratio, are more significant than the volume. However, it should be noted that the effect of the volume cannot be completely neglected because there is evidence of its high significance from the interactions with the diameter ratio and the immersion depth ratio.
Fig. 4. ANOVA results.
From the DOE results, it is understood that the volume of the liquid has less significance on the cavitation zone size. Therefore, the total volume of the liquid was selected as a constant value of 57 cc to conduct the parametric analysis. The goal was to identify the optimal geometric configuration that gives the maximum cavitation zone size inside the ultrasonic processing cell within the considered ranges. The parametric analysis was conducted in two steps: • Step 1: The immersion depth ratio of 0.5 was selected, and the diameter ratio was varied from 1.25 to 4.0 with an increment of 0.25. • Step 2: In this step, the diameter ratio was set to a constant value obtained from the result in the previous step. The immersion depth ratio, on the other hand, was changed from 0.125 to 4.0 with an increment of 0.125. The plot in Fig. 5(a) shows the variation in the values of equivalent diameters for a change in D/DP values. It can be seen that there is a high dependence of the cavitation zone size on the diameter of the ultrasonic cell. As we move from the left to the right of the plot, the distance between the side wall of the cell and the probe surface is increasing. When this distance is small the effect of reflection from the side wall is strong, due to constructive interference. As we move towards the right end of the plot, the equivalent diameter becomes smaller, as the side wall gets farther from the probe. The bottom wall is also expected to have a similar effect. However, from the plot it can be seen that initially when the bottom wall is at a much farther distance the equivalent diameter is much higher. Towards the right, the equivalent diameter value decreases although the bottom wall is at a closer distance from the probe. The equivalent diameter is consistent at a certain level until it suddenly starts decreasing starting from D/DP = 1.65. With the selected value of 2.8 for the diameter ratio, the immersion depth ratio was changed from 0.125 to 4.0 with an increment of 0.125. Fig. 5(b) shows that the equivalent diameter of the cavitation zone rapidly increases with increasing the immersion depth ratio, and then the slope levels off as the ratio closes to 1. The reasons would be the interference of the ultrasound waves and their reflections inside the ultrasonic processing cell. The largest equivalent diameter is 2.63 cm for the immersion depth ratio of 2.0. As we move toward the right on the plot in Fig. 5(b), we can see a gradual increase in the equivalent diameter value up to d/DP = 2.0, followed by gradual reduction until d/DP = 4.0 only to be improved again until the end. Initially, the divergence of the reflected ultrasonic wave from the sidewall is limited by space. As the depth keeps increasing, there is more space available. So when the immersion depth increases, there will be multiple reflections between the ultrasonic processing cell side wall and the probe side wall resulting in different interference patterns. This can be observed in Fig. 5(b) when d/DP = 2.25. The cavitation zone extends into the narrow channel between the side wall and the probe wall. Fig. 6 shows the drastic change in cavitation zone size with a change in diameter ratio of 0.05. As the diameter ratio increases, the distance between the side walls and the source keeps increasing and at D/DP = 1.90, the constructive interference ceases thereby leading to a poor cavitation zone size. The DOE results clearly show that the diameter ratio is more significant than the immersion depth ratio. Therefore, the parametric analysis was first conducted with respect to the diameter ratio to find the appropriate value within the considered range (from 1.25 to 4.0). The results from this step show the variation of the equivalent diameter of the cavitation zone with varying diameter ratio as shown in Fig. 6. The drastic variations in the cavitation zone size
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Fig. 5. Equivalent diameter of the cavitation zone with varying (a) diameter ratio and (b) immersion depth ratio.
Table 3 Measurements of micro-hardness and surface porosity area. Sample no. 1 2
Micro hardness (HRC) 74 ± 8.7 72 ± 4.7
Surface porosity area (in.2 ) 0.077342 0.041369
From both the above analyses, the parameters of D/DP = 2.80, d/DP = 2.0 for a volume of 57 cc were identified to give the maximum cavitation zone size. 5. Experimental
Fig. 6. Cavitation zone size variation with change in diameter ratio.
Fig. 7. Cavitation zone when volume = 57 cc: (a) D/DP = 2.80, d/DP = 0.25 and (b) D/DP = 1.5, d/DP = 2.25.
can be attributed to the interference of ultrasound waves and their multiple reflections from the cell walls. It is to be noted that the diameter ratio of 2.80 gives the largest equivalent diameter, which is 2.15 cm. The increment in the cavitation size is a direct consequence of the reflection of the ultrasonic waves by the probe side walls. Initially when the d/DP is small, the cavitation zone is small and confined to the region around the probe surface (as shown in Fig. 7). We see a gradual increase in its size as the immersion depth increases. The diameter ratio is constant and so the sidewall and the probe are at a constant distance. The change is only in the depth of the probe wall. The reflections between the probe wall and the side wall can be attributed to causing this change in cavitation zone size.
An experiment was performed to study the effectiveness of ultrasonic processing using the geometric parameters determined in the computational modeling results. The experimental procedure and setup is closely followed from previously published work [25]. A master nanocomposite was prepared by Foosung Precision Industry Co., Ltd. (South Korea). It consisted of aluminum alloy A4000 (Al-11.5 Si-4.25 Cu-0.65 Mg) as the base matrix. The nanomaterials in the sample consisted of a hybrid powder comprised of carbon nanofibers (150 nm diameter, 6 m length) (CM-150, Hanwha Chemical, South Korea) and SiC micropowders (5.5 m diameter) (Greendensic GC, Showa Denko K.K, Japan). The ultrasonic source used in this experiment was a Q700 Sonicator system (Qsonica, USA). A K-type thermocouple with ceramic shielding was used to monitor the temperature of the melt. The melt zone consisted of a graphite crucible (3.6 cm diameter, 7.8 cm height), which was heated with an electric resistive heating furnace. The furnace environment was shielded with a supply of Argon gas. A schematic of the experimental setup is shown in Fig. 8. Two different samples were prepared in this experiment, by melting the Al alloy without and with ultrasonic processing. The Al alloy master nanocomposite was melted in the furnace and then poured into a stainless steel mold to prepare a disk-shaped sample (63.5 mm diameter, 12.7 mm thickness). A second sample was prepared by subjecting the Al alloy melt to ultrasonic processing with an amplitude of 60% for 15 min. The ultrasonic probe was placed inside the melt at depth of 1 (2.54 cm), following a d/Dp ratio of 2.0. The melt was then poured into the mold when the melt temperature reached 740 ◦ C. Images of the samples are shown in Fig. 8(b). A Rockwell hardness tester (hardness scale ‘C’) was used to measure the micro-hardness of the produced samples. As observed from Table 3, there was a 46% reduction in the deviation of micro hardness data in Sample 2 compared to Sample 1. This reduction indicates better homogeneous dispersion and distribution of the nanomaterials within the MMNC, due to ultrasonic processing. The surface porosity area was measured from the images of the surface of the collected samples using an image processing software, ImageJ (NIH, USA). A 50% reduction in the total
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Fig. 8. (a) Schematic of the experimental setup, (b) images of produced samples.
area of the surface pores was observed in Sample 2. In a cast part, gas porosity presents itself on the surface of the metal. So the area of the surface pores can be considered as the extent of dissolved gases present inside the sample. Ultrasonic processing can remove dissolved gases within cast parts [4]. So, the reduction in the surface pore area is an indication of the effectiveness of acoustic cavitation for material processing. 6. Conclusions A computational model was developed using the finite element method to resolve the acoustic pressure field inside the ultrasonic processing cell. Non-linear effects such as viscous losses and discontinuous boundary conditions were studied for the modeling, and the model was successfully validated using experimental results. The acoustic cavitation zones were quantitatively measured and compared with different geometric configurations of the ultrasonic processing cell. ANOVA and parametric analysis were used to investigate the dimensional effects on the acoustic cavitation involved in the ultrasonic processing. It was found that the two newly introduced parameters had significant effects on the cavitation zone size − the ratio of the ultrasonic processing cell diameter to the ultrasonic probe diameter (D/Dp ) and the ratio of the probe immersion depth to the ultrasonic probe diameter (d/Dp ). From the parametric analysis for a constant volume of 57 cc, it was observed that the ultrasonic processing cell with the geometric parameters of D/DP = 2.8 and d/DP = 2.0 provided the largest acoustic cavitation area within the studied ranges. Aluminum alloy A4000 MMNC with carbon nanofibers and SiC microparticles was used to study the effect of ultrasonic processing with decided parameters on its hardness. The sample treated by the ultrasonic processing showed a 45.98% reduction in the standard deviation of the hardness measurement and a reduction of 46.52% in total surface porosity area, which clearly shows the effect of ultrasonic processing with the determined geometric parameters on material properties. Acknowledgement The authors thank Youngsek Yang at Research Center of Foosung Precision Ind. Co., Ltd. (South Korea) for the materials used in study. References [1] Martini S. Introduction. Sonocrystallization of fats. NY: Springer New York; 2013. p. 1–5. [2] Casati R, Vedani M. Metal matrix composites reinforced by nano-particles—a review. Metals 2014;4:65–83.
[3] Koli DK, Agnihotri G, Purohit R. Influence of ultrasonic assisted stir casting on mechanical properties of Al6061-nano Al2 O3 composites. Mater Today: Proc 2015;2:3017–26. [4] Zulfia A, Salahuddin J, Ahmad HE. Characterization of Al–Si–Mg/Al2 O3 nanocomposite produced by stir casting method. Mater Sci Forum 2015;827:294–9. [5] Yan J, Xu Z, Shi L, Ma X, Yang S. Ultrasonic assisted fabrication of particle reinforced bonds joining aluminum metal matrix composites. Mater Des 2011;32:343–7. [6] Wang Z, Wang X, Zhao Y, Du W. SiC nanoparticles reinforced magnesium matrix composites fabricated by ultrasonic method. Trans Nonferrous Metals Soc China 2010;20:s1029–32. [7] Yang Y, Li X. Ultrasonic cavitation based nanomanufacturing of bulk aluminum matrix nanocomposites. J Manuf Sci Eng 2007;129:497. [8] Lan J, Yang Y, Li X. Microstructure and microhardness of SiC nanoparticles reinforced magnesium composites fabricated by ultrasonic method. Mater Sci Eng A 2004;386:284–90. [9] Merouani S, Hamdaoui O, Rezgui Y, Guemini M. Optimum bubble temperature for the production of hydroxyl radical in acoustic cavitation–frequency dependence. Acta Acust United Acust 2015;101:684–9. [10] Kubo T, Kuwabara M, Yang J. Visualization of acoustically induced cavitation bubbles and microjets with the aid of a high-speed camera. Jpn J Appl Phys 2005;44:4647–52. [11] Sáez V, Frías-Ferrer A, Iniesta J, González-García J, Aldaz A, Riera E. Characterization of a 20 kHz sonoreactor. Part I: analysis of mechanical effects by classical and numerical methods. Ultrason Sonochem 2005;12:59–65. [12] Kumar A, Gogate PR, Pandit AB. Mapping the efficacy of new designs for large scale sonochemical reactors. Ultrason Sonochem 2007;14:538–44. [13] Lee J, Ashokkumar M, Yasui K, Tuziuti T, Kozuka T, Towata A, et al. Development and optimization of acoustic bubble structures at high frequencies. Ultrason Sonochem 2011;18:92–8. [14] Gogate PR, Shirgaonkar IZ, Sivakumar M, Senthilkumar P, Vichare NP, Pandit AB. Cavitation reactors: efficiency assessment using a model reaction. AIChE J 2001;47:2526–38. [15] Kesh S. Fundamentals of acoustics. Perth, Australia: Technical Publications Trust; 1982. [16] Servant G. Numerical simulation of cavitation bubble dynamics induced by ultrasound waves in a high frequency reactor. Ultrason Sonochem 2000;7:217–27. [17] Servant G, Laborde J-L, Hita A, Caltagirone J-P, Gérard A. Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results. Ultrason Sonochem 2001;8:163–74. [18] Schanz D, Metten B, Kurz T, Lauterborn W. Molecular dynamics simulations of cavitation bubble collapse and sonoluminescence. N J Phys 2012;14: 113019. [19] Nakatani S, Yoshida K, Watanabe Y. Optical and acoustic observations of bubble adhered to piezoelectric transducer under ultrasound field: pressure signal caused by bubble behavior. Jpn J Appl Phys 2008;47:3904–7. [20] Dähnke S, Keil FJ. Modeling of three-dimensional linear pressure fields in sonochemical reactors with homogeneous and inhomogeneous density distributions of cavitation bubbles. Ind Eng Chem Res 1998;37:848–64. [21] Dähnke S, Swamy KM, Keil FJ. Modeling of three-dimensional pressure fields in sonochemical reactors with an inhomogeneous density distribution of cavitation bubbles. Ultrason Sonochem 1999;6:31–41. [22] Caflisch RE, Miksis MJ, Papanicolaou GC, Ting L. Wave propagation in bubbly liquids at finite volume fraction. J Fluid Mech 1985;160:1–14. [23] Klíma J, Frias-Ferrer A, González-García J, Ludvík J, Sáez V, Iniesta J. Optimisation of 20 kHz sonoreactor geometry on the basis of numerical simulation of local ultrasonic intensity and qualitative comparison with experimental results. Ultrason Sonochem 2007;14:19–28.
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[24] Bargoshadi JA, Najafiaghdam E. Ultrasonic dispersion system design and optimization using multiple transducers. In: 2009 symposium on piezoelectricity, acoustic waves, and device applications (SPAWDA 2009). 2009. p. 96. [25] Sutkar VS, Gogate PR, Csoka L. Theoretical prediction of cavitational activity distribution in sonochemical reactors. Chem Eng J 2010;158:290–5. [26] Thiemann A, Nowak T, Mettin R, Holsteyns F, Lippert A. Characterization of an acoustic cavitation bubble structure at 230 kHz. Ultrason Sonochem 2011;18:595–600. [27] Raman V, Abbas A, Joshi SC. Mapping local cavitation events in high intensity ultrasound fields. In: Proceedings of the COMSOL users conference. 2006.
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[28] Lin S, Zhang F. Measurement of ultrasonic power and electro-acoustic efficiency of high power transducers. Ultrasonics 2000;37:549–54. [29] Young FR. Cavitation. McGraw-Hill; 1989. [30] Leighton T. The acoustic bubble. Academic Press; 1997. [31] Brennen CE. Cavitation and bubble dynamics. Oxford University Press; 1995. [32] Chen L-Y, Peng J-Y, Xu J-Q, Choi H, Li X-C. Achieving uniform distribution and dispersion of a high percentage nanoparticles in Mg18Sn matrix by solidification processing. In: Magnesium Technology 2014. 2014. p. 465–70. [33] Tajik B, Abbassi A, Saffar-Avval M, Abdullah A, Mohammad-Abadi H. Heat transfer enhancement by acoustic streaming in a closed cylindrical enclosure filled with water. Int J Heat Mass Transf 2013;60:230–5.
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Technical Paper
The effect of geometrical parameters on the characteristics of ultrasonic processing for metal matrix nanocomposites (MMNCs) Pavan Pasumarthi, Saheem Absar, Hongseok Choi ∗ Department of Mechanical Engineering, Clemson University, Clemson, SC, United States
a r t i c l e
i n f o
Article history: Received 16 December 2015 Received in revised form 29 March 2016 Available online xxx Keywords: Metal matrix nanocomposites Ultrasonic processing Dimensional effect Acoustic cavitation Helmholtz equation
a b s t r a c t Metal matrix nanocomposites (MMNCs) can offer significant improvement of properties such as higher specific strength, specific modulus, controlled thermal expansion and higher corrosion resistance, compared to the base metallic materials. However, agglomeration or clustering of nanomaterials makes it very difficult to disperse them in the metal matrix. Non-linear effects of ultrasonic processing, such as acoustic cavitation and acoustic streaming, help in the dispersion and distribution of the nanomaterials. Non-linearity of the ultrasonic processing makes it very hard to measure or characterize the process experimentally. There is very limited knowledge about the interactions between the geometrical parameters of the ultrasonic processing and the extent of cavitation achieved. Numerical modeling offers powerful tools to overcome the experimental difficulties involved. In this study, a non-linear numerical model was developed to resolve the acoustic pressure field, and the cavitation zone size was quantified from the numerical modeling results. The model was then used to study the effect of geometry on the cavitation zone size. Analysis of variance (ANOVA) was used to identify the significant parameters. A parametric analysis involving these parameters was subsequently performed. A configuration of geometrical parameters offering the highest cavitation zone size was determined. It was found out that a probe immersion depth of 25.4 mm produced a maximum cavitation zone in the ultrasonic processing cell with a diameter of 35.9 mm for processing 57 ml of molten Al alloy. An experimental validation has been accomplished by ultrasonically processing an aluminum alloy with carbon nanofibers and silicon carbide microparticles. With selected parameters the area of micro pores in the MMNC was significantly decreased by 50% and a deviation of the hardness was also decreased by 46% due to further dispersion and distribution of the carbon nanofibers. © 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Ultrasound with a frequency above 20 kHz can be classified into two groups: power ultrasound and diagnostic ultrasound based on its frequency range [1]. For material processing applications such as degassing, mixing, synthesis, or liquid metal treatment, the power ultrasound (20 kHz to 2 MHz) is more suitable than the diagnostic one [1] due to its higher amplitude and non-linear effects like acoustic cavitation and acoustic streaming. In the current study, ultrasound with the frequency of 20 kHz was used to disperse and distribute nanomaterials to manufacture metal matrix nanocomposites (MMNCs) which are advanced materials incorporated with nanomaterials as reinforcements [2]. MMNCs have shown enormous potential especially in structural applications, by offering
∗ Corresponding author. E-mail addresses: [email protected] (P. Pasumarthi), [email protected] (S. Absar), [email protected] (H. Choi).
excellent strength to weight ratio, along with mechanical properties such as ductility, fatigue, hardness, etc., showing significant improved properties compared to the base materials [2]. Currently, the manufacturing technologies of MMNCs can be classified into solid- and liquid-base processes [2]. Among those technologies, the liquid-base process is the most efficient and cost-effective method. However, it is very difficult to uniformly disperse nanomaterials in molten metal using conventional stirring methods because the shear stresses generated are not enough to break the bonding strength of the nanomaterials caused by mutually attractive van der Waals forces [2–4]. Ultrasonic processing utilizes non-linear effects such as acoustic cavitation and acoustic streaming, to disperse and distribute the nanomaterials in molten metals. This process shows promising results with relatively uniform dispersion and distribution of the nanomaterials in various metal matrices [5–8]. The acoustic cavitation can generate enough stress to break the agglomeration of the nanomaterials and the acoustic streaming can produce enough flow to disperse them in the molten metal. The acoustic cavitation is a generation of gas bubbles that occur
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during the rarefaction cycles of the acoustic pressure wave during ultrasonic processing. Under the subsequent ultrasound field, the cavities pulsate until reaching a critical radius after which they implode. The trapped air pockets in the nanomaterial clusters also act as the cavitation seed nuclei, from which cavitation bubbles originate. During the implosion the released shock waves break apart the clusters, leaving nanomaterials dispersed throughout the liquid metal. The dispersed nanomaterials are distributed homogenously by the acoustic streaming flow. It should be noted that the collapse of cavitation bubbles results in the generation of extremely high temperatures and pressures [9], and a micro-jet is also reported to be observed [10]. But, these implosions are very short lived (in the order of pico-seconds) and extremely localized. Acoustic streaming is a non-linear consequence of the attenuation of ultrasonic wave during its propagation. The ultrasonic wave attenuates very rapidly in a short space interval [11]. The attenuation of the wave generates a pressure difference in the liquid that generates flow. A system for the ultrasonic processing of liquids consists of two principal parts: an excitation source and a liquid load. The excitation source produces an ultrasonic energy, which is then delivered to the liquid through an ultrasonic probe. The liquid is contained in a vessel that is termed an ‘ultrasonic processing cell’. The ultrasonic processing cell can be made of different materials depending on the applications. There are several factors that affect ultrasonic processing of liquids. Appropriate design and configuration of the ultrasonic processing equipment is very critical for the effectiveness of ultrasonic processing. In current practice of the ultrasonic processing of liquids, the processing parameters are mainly selected by heuristic arguments or based on the experience of operators. The experimental knowledge is extremely limited and highly subjective because of the process dependence on the physical parameters such as the dissolved gas content. Kumar et al. [12] quantified the uniformity of cavitation field by introducing a new quantity called the degree of uniformity. In their work, hydrophones were used to make the measurements. However, the hydrophones inside the liquid can have microscopic pockets of air trapped on their surfaces and they will interfere with the acoustic cavitation process. Lee et al. [13] took high speed photographs of the bubble structures, but they were unable to extract holistic information that can explain the mechanism of the acoustic cavitation. Gogate et al. [14] calculated the efficiency of the cavitation reactors by using a model reaction. The repeatability of the process is poor because the purity of the liquid used is not considered. On the other hand, various numerical models of the acoustic pressure field inside the sonochemical reactor have been intensively developed. Most of them simulate the acoustic pressure field in the sonochemical reactor filled with water. They are based on the linearization of the Euler equations [15], which generate the Helmholtz equation for the ultrasonic wave propagation. The linear Helmholtz equation is very robust and easily solvable using finite element method (FEM). Recently, attempts have been made to simulate cavitation formation and implosion inside the reactor [16–18]. It should be noted that there is an uncertainty involved in the models because of the time variation and spatial scales in the cavitation process. However, several authors have studied the modeling and prediction of the cavitation distribution inside the sonochemical reactor [19–21]. They are based on the linearization of Caflisch equations, which is a widely accepted notion that relates the cavitation bubble fraction at any point to the corresponding acoustic pressure [22]. Based on the previous research on the pressure field inside the sonochemical reactor [11,23,24], in this study, the cavitation formation and implosion is characterized using the numerical model which was developed to resolve the acoustic pressure field inside the ultrasonic processing cell. The
numerical model is then used to investigate the dimensional effect of different geometric configurations of the ultrasonic processing cell and the position of the ultrasonic probe on acoustic cavitation. Finally, an experimental validation is conducted to verify the developed numerical model. 2. Numerical modeling The following wave equation [11] describes the acoustic pressure variation in space and time, as given in Eq. (1):
∇
1
∇P −
2
1 ∂ P = 0, c 2 ∂t 2
(1)
where P is the acoustic pressure, is the density, c is the speed of sound, and t is the time. Since most ultrasound sources emit sinusoidal waves, assuming the pressure wave is harmonic in nature is quite reasonable, P(r, t) = p(r) · eiωt ,
(2)
where ω is the angular frequency of the ultrasonic wave and is given by ω = 2f, where f is the frequency in Hz, and r describes the position in (x, y, z) coordinates. Substituting Eq. (2) in Eq. (1), the linear homogenous wave equation can be obtained, which is only dependent on the spatial variable r:
∇
1
∇P −
2
ω2 ∂ P =0 c 2 ∂t 2
∇ 2 P + k2 P = 0
(3) (4)
Eq. (4) is known as the Helmholtz equation with acoustic pressure P, wave number k given by Eq. (5): k=
ω c
(5)
Although the above linear model describes the geometric attenuation due to multiple reflections and wave dispersion, it ignores the attenuation due to the liquid properties. To describe the damping properties of a medium, the complex sound speed, cc and the complex density, c of the medium are defined as follows [15]:
cc = c
c =
4
1 + iω
c 2 cc2
3
+ b
0.5
c 2
,
(6)
(7)
where is the dynamic viscosity and b is the bulk viscosity of the medium. 2.1. Modeling geometry An axisymmetric geometric section of the ultrasonic processing cell and the ultrasonic probe was modeled, which is shown in Fig. 1(a). The ultrasonic probe is immersed into the liquid up to a height d. The cell geometry is given by diameter D and height H. The probe diameter is Dp . The parameters for the modelling were obtained from experimental results published by Sutkar et al. [25], where they used a hydrophone to measure the acoustic pressure values along the axis of the ultrasonic processing cell. 2.2. Boundary conditions The ultrasound waves propagate differently in different media. Impedance of the medium is the material property that dictates the
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Fig. 1. (a) Axisymmetric geometrical model and (b) chosen boundary conditions, including unstructured mesh.
propagation characteristics of the ultrasound wave. Impedance of the medium is given by Eq. (8): Z = × c,
(8)
where is the density of the medium and c is the speed of sound in the medium. Several researchers have attempted to resolve the numerical models using either infinitely hard or partially reflecting boundaries [26]. However, the hard and soft boundaries are idealized cases. In practice, almost all the boundaries are considered as ‘discontinuous boundaries’. The discontinuity is in the impedance. As the sound wave propagates across the boundary between two different media, it experiences a change in the impedance of the medium. This affects the propagation characteristics of the ultrasound wave. One way to quantify the impedance mismatch is to calculate the reflection coefficient at the interface given by the following expression [23], given by Eq. (9): Rce =
Z − Z 2 2 1 Z2 + Z1
,
(9)
where Z1 and Z2 are the impedances of the two media. The pressure field that is generated inside the ultrasonic processing cell is the resultant of interactions between the reflected waves from the boundaries and the incident ultrasound wave. The chosen boundary conditions for the model are shown in Fig. 1(b). The side walls of the ultrasonic probe that are immersed in water are modeled as rigid walls. Mathematically it can be represented by Eq. (10):
∂p = 0, ∂n
(10)
where n is the plane normal to the boundary. The boundaries between interfaces are given using the impedance boundary condition. There are two interfaces in the current reactor: the interface between water and glass, and the interface between water and air. The tip surface of the ultrasonic probe is modeled as a pressure boundary condition [27]. The pressure amplitude at the probe surface can be given by Eq. (11): Pa =
2Ic,
(11)
where Pa is the pressure amplitude of the ultrasonic probe, is the density of water and c is the speed of sound in water. I is the intensity of the power input into the medium, given by Eq. (12): I = I0 × ,
(12)
where is the factor of conversion of the ultrasonic probe assumed to be around 0.85 [28] and I0 is the intensity of power input into the ultrasonic probe. 2.3. Discretization In finite element modelling of the acoustic pressure field, the node length should satisfy the following condition [27], given by Eq. (13):
h
l
1,
(13)
where hl is the node length, which is the size of the longest side of the triangular mesh element and is the wavelength of the sound wave. In order to conserve computational resources, an unstructured mesh was utilized. The region closer to the probe tip surface has much finer meshes than ones in other areas of the domain, as shown in Fig. 1(b). The longest node length in this case is 0.0128 cm, which satisfies the condition specified by Eq. (13). The unstructured mesh was selected because of the fact that the cavitation zone is often concentrated in the region immediately below the probe tip surface [1]. The finer discretization around the probe tip surface was applied to a round area with a diameter of about /10 [7]. 3. Numerical results The finite element model for calculating the acoustic pressure field inside the ultrasonic processing cell was solved using the commercial FEM package, COMSOL Multiphysics 5.1. 3.1. Acoustic pressure field In order to study the effect of the boundary conditions on the acoustic pressure field, an analysis with two different boundary condition configurations was performed. In the first configuration, the side walls were considered to be infinitely hard and the top boundary was considered as a soft boundary. In the second configuration, both the side walls and the top wall were considered to be partially reflecting. There is an impedance mismatch between the media that is being considered. The surface of the ultrasonic probe remained as infinitely hard in both cases. The impedance mismatch between water and the titanium ultrasonic probe is excessively high, hence majority of the ultrasonic waves reflect back, and very little passes through the interface.
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4 Table 1 Parameters for the numerical model. Parameter
Value
D, cm DP , cm H, cm d, cm t, cm Frequency, Hz P, W
13.5 2 17 2 0.3 20,000 36
It was observed that the boundary conditions have an impact on the resultant acoustic pressure field. The ultrasound wave is partially transmitted through the boundary and the rest is reflected back into the ultrasonic processing cell. Since the glass wall has higher acoustic impedance compared to water, the majority of the ultrasound wave is reflected back but a portion of them is transmitted through the glass wall. The transmitted waves travel to reach the next boundary. At the interface between glass and air, the ultrasonic waves once again undergo partial reflection. While the ultrasonic waves leave the glass wall (higher acoustic impedance) into the air (lower acoustic impedance), the majority of the ultrasound waves are transmitted through the interface while a minor portion is reflected back. The reflected waves inside the glass wall undergo multiple reflections, and then some of them return into the water and start interacting with the existing ultrasound waves. The final boundary conditions selected for this model are shown in Fig. 1(b). The results clearly showed that the area of higher acoustic pressure magnitude inside the ultrasonic processing cell is relatively larger than that the cases considering either infinitely hard or partially reflecting walls as boundary conditions. 3.2. Validation The numerical results from the non-linear acoustic pressure field model was validated by comparing to those reported by Sutkar et al. [25], consisting of experimental measurements of the acoustic pressure along the axis of a sonochemical reactor, measured using hydrophones. As explained in the previous section, an FEM model for calculating the acoustic pressure field inside the ultrasonic processing cell has been developed. The geometric and operational parameters used are listed in Table 1. The ultrasonic processing cell was made of borosilicate glass, a standard thickness of 0.3 cm, with a diameter of 13.5 cm and the liquid level was 17 cm. The probe was positioned at 2 cm below the water surface. An ultrasonic source of 20 kHz and a power of 36 W were used. The model was solved using the commercial FEM package, COMSOL Multiphysics 5.1 (COMSOL, USA). Meshing was performed based on the previous discussion. The additional glass thickness is also meshed similar to the liquid domain adjacent to it. The mesh is shown in Fig. 1(b). The wall thickness of 0.3 cm is very small compared to the wavelength of the ultrasonic wave, so a relatively coarser mesh used in the wall thickness would be appropriate to capture the acoustic pressure wave. Fig. 2(a) clearly shows that the pressure along the axis from the simulation result is reasonably similar to the reported experimental measurements. The resultant acoustic pressure field obtained from the numerical model is shown in Fig. 2(b). The experimental measurements of the acoustic pressure along the axis of a sonochemical reactor were conducted using hydrophones [25]. The measurements start at a distance of 1 cm from the probe tip surface and continue at 14 different points with the last measurement taken at 14 cm. The solid line represents the experimental measurements, and the dashed line shows the numerical calculations. An error
analysis revealed that the mean error is about 33%, with a maximum error of 78% at a point 2 cm away from the probe tip surface and a minimum error of 5.8% at a point 4.5 cm away from the probe tip surface. It can be observed that the difference between the numerical results and the experimental measurements is larger when the measurement is close to the probe tip surface and the bottom surface of the ultrasonic processing cell. This would be caused by the fact that when the hydrophone is close to the probe tip surface or the bottom surface of the ultrasonic processing cell, the interference caused by the existence of the hydrophones would be constructive. The difference would be proportional to the distances between the hydrophone and the probe tip surface and the ultrasonic processing cell bottom surface. 3.3. Characterization of cavitation zone While the acoustic pressure field is a useful result, there is no directly available information about the cavitation formation and implosion inside the ultrasonic processing cell. It is known that cavitation only takes place at locations where the acoustic pressure is above the threshold pressure. In this study, the cavitation area is used to quantify the cavitation formation and implosion inside the ultrasonic processing cell. Cavitation is the generation of gas filled cavities inside a fluid. There are two types of acoustic cavitation that are reported [29]: • Stable cavitation: involves the oscillation of bubbles in the ultrasonic field whose size is close to their equilibrium bubble sizes. These oscillations typically last several acoustic cycles and are generally larger in size than transient bubbles. • Transient cavitation: involves bubbles of several different sizes oscillating volumetrically (expanding and contracting) in the ultrasonic field. The oscillations continue until the cavities reach a critical radius upon which they implode. The implosion events generate shockwaves and micro-jets, which are accompanied by tremendous amount of pressure (few hundred atmospheres) and high temperatures (few thousand K). These extreme conditions occur in highly localized areas and are retained for extremely short time (ps). Cavitation occurs during the rarefaction cycle of the ultrasound pressure wave. Theoretically, when the negative pressure exceeds the threshold pressure, voids are formed in the liquid. The dissolved gas inside the liquid diffuses into the void forming a gas cavity [30]. The transient cavitation threshold value in several liquids has been investigated by several authors over the years. However, in practice, every liquid has dissolved gases in the form of micron sized cavities which act as the seed nucleus for the cavitation under the sound field [30]. Blake developed an equation for calculating the cavitation threshold by incorporating the equilibrium bubble radius into the term [30] given by Eq. (14). The ‘equilibrium bubble radius’ is the radius at which a gas bubble is stable in a given liquid in the absence of an external sound field. This is in fact the radius of the seed nuclei that act as the cavitation spots [30,31]. 4
× Pb = P0 − Pv + 3
2 × 3 P0 +
2
R0
− Pv × R0 3
(14)
where Po is the ambient pressure which is 101,325.23 Pa, Pb is the cavitation threshold pressure, Pv is the vapor pressure of water which is 3,173.032 Pa, is the surface tension of water, 73.0 mN/m, and Ro is the equilibrium radius of the cavitation bubbles, 0.08 m [30]. All the properties of water were taken at 298 K. The threshold pressure for cavitation was found to be 0.8 MPa. Using this value, the regions inside the ultrasonic processing cell where the acoustic
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Fig. 2. (a) Validation of numerical model with experimental results from [25], (b) Resolved acoustic pressure field.
the height of the ultrasonic processing cell, rather the height of the liquid inside the ultrasonic processing cell. When the ultrasonic probe is immersed into the liquid, there is a rise in the liquid level and it changes the value of H. Fig. 1(a) illustrates all geometrical parameters and determination of each parameter is given below: • Real height, H: This is the final height of the liquid level when the ultrasonic probe is immersed into the liquid, including the height rise (H), given by Eq. (15): H = H + H
(15)
• Nominal height, H : This is the height of the liquid level before the ultrasonic probe is inserted into the liquid, given by Eq. (16): H = Fig. 3. Typical plot for the cavitation zone measurement.
pressure exceeds the threshold were identified, as shown in Fig. 3. The dark region is the cavitation zone in which the cavitation will occur, and the white regions have little probability of cavitation formation. It should be noted that it is very challenging to exactly anticipate the location of cavitation bubble generation. The cavitation zone location is the most exhaustive information which can be obtained from the acoustic pressure field. In order to compare the cavitation zones in different geometrical configurations of the ultrasonic processing cell and the position of the ultrasonic probe, two new mathematical quantities were defined in this study (shown in Fig. 3): • Equivalent area (Aeq ): The area of a circle which has same area as of the cavitation zone in a particular configuration. • Equivalent diameter (Deq ): It is the diameter of the circle whose area is given by equivalent area (Aeq ). 4. Design of experiments for geometrical parameters There are various geometrical parameters involved in ultrasonic processing. Cell dimensions such as the ultrasonic processing cell diameter (D), height (H) and volume (V) and the ultrasonic probe position - given by its immersion depth (d) and diameter (Dp ) are important. The probe diameter (Dp ) was kept as a constant value of 1.27 cm. It is to be noted that the height (H) does not represent
4×V × D2
(16)
• Rise height, H: This is the rise in the liquid level after the ultrasonic probe is immersed into the liquid, given by Eq. (17): H =
0.5 × Dp3 D2
(17)
Two new geometrical parameters defined as diameter ratio (D/DP ) and immersion depth ratio (d/DP ) were introduced in this study. The three parameters – diameter ratio, immersion depth ratio and liquid volume are of interest to investigate the effect of the geometrical parameters on ultrasonic processing. 4.1. ANOVA In order to find the optimal geometric configuration and reduce the number of simulations in the parametric analysis, the statistical technique of analysis of variance (ANOVA) was employed. The three geometrical parameters – diameter ratio, immersion depth ratio and volume were considered as the three factors whereas the equivalent diameter (Deq ) was considered to be the response variable. The goal of the study was to find out the factors that are more significant in determining the response variable, Deq. For a full factorial experiment with 3 factors and 3 levels, a total of 27 runs were performed. Each factor has a high level, a low level and a mid-point. Selection of the high and low levels for factors is a very important aspect of ANOVA. For the diameter ratio, a lower level of 1.25 was selected considering the physical feasibility of the
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6 Table 2 Factors and 3 levels selected for DOE.
4.2. Parametric analysis
Factor
Low level (−1)
Mid-point (0)
High level (+1)
(D/DP ) (d/DP ) Volume (cc)
1.25 0.25 50
2.25 1.625 125
3.0 3.0 200
set-up. A (D/DP ) value of 1.25 gives an ultrasonic processing cell diameter of 1.5875 cm for an ultrasonic probe with a diameter of 1.27 cm. This leaves a gap of 0.15875 cm between the sides of the probe and the inside walls of the ultrasonic processing cell. A gap less than 0.15875 would not be practical for an experimental setup. The high level was selected to be 3.0 from the literature [32]. It has been reported that the radial variation of acoustic pressure field is very pronounced when the distance between the probe center and the inside walls is less than 1.5 times the probe diameter. Above this point there is a significant decrease in ultrasonic power intensity. For the immersion depth ratio, the lower level of 0.25 was selected. This gives an immersion depth of 0.3175 cm. Although it is only a quarter of the probe diameter, the ultrasonic probe would still transmit ultrasound waves into the liquid. With a shallower immersion depth below this point, however, the coupling of the ultrasonic waves with the liquid is expected to be very poor. A higher level of 3.0 was selected for the (d/DP ) value based on the design limit for the immersion depth of the ultrasonic probe in a sonochemical reactor [33]. The lower and the higher volume limits were selected to be 50 cc and 200 cc, respectively. When the volume is 50 cc with (D/DP ) of 3.0, it gives the real height of 4.445 cm, which allows a gap of only 0.635 cm between the tip surface of the ultrasonic probe and the bottom surface of the ultrasonic processing cell for the immersion depth ratio of 3.0. Similarly the higher level of volume was selected to be 200 cc. The selected factors and levels for this study are shown in Table 2. A total of 27 different geometrical configurations were solved for the response variable, Deq . A plot of standardized effects based on the ANOVA results is shown in Fig. 4. Significance is determined based on the distance of each point from the normal line. The farther a point is from the line, the more it influences the response variable. It can be clearly observed that two factors - the diameter ratio and immersion depth ratio, are more significant than the volume. However, it should be noted that the effect of the volume cannot be completely neglected because there is evidence of its high significance from the interactions with the diameter ratio and the immersion depth ratio.
Fig. 4. ANOVA results.
From the DOE results, it is understood that the volume of the liquid has less significance on the cavitation zone size. Therefore, the total volume of the liquid was selected as a constant value of 57 cc to conduct the parametric analysis. The goal was to identify the optimal geometric configuration that gives the maximum cavitation zone size inside the ultrasonic processing cell within the considered ranges. The parametric analysis was conducted in two steps: • Step 1: The immersion depth ratio of 0.5 was selected, and the diameter ratio was varied from 1.25 to 4.0 with an increment of 0.25. • Step 2: In this step, the diameter ratio was set to a constant value obtained from the result in the previous step. The immersion depth ratio, on the other hand, was changed from 0.125 to 4.0 with an increment of 0.125. The plot in Fig. 5(a) shows the variation in the values of equivalent diameters for a change in D/DP values. It can be seen that there is a high dependence of the cavitation zone size on the diameter of the ultrasonic cell. As we move from the left to the right of the plot, the distance between the side wall of the cell and the probe surface is increasing. When this distance is small the effect of reflection from the side wall is strong, due to constructive interference. As we move towards the right end of the plot, the equivalent diameter becomes smaller, as the side wall gets farther from the probe. The bottom wall is also expected to have a similar effect. However, from the plot it can be seen that initially when the bottom wall is at a much farther distance the equivalent diameter is much higher. Towards the right, the equivalent diameter value decreases although the bottom wall is at a closer distance from the probe. The equivalent diameter is consistent at a certain level until it suddenly starts decreasing starting from D/DP = 1.65. With the selected value of 2.8 for the diameter ratio, the immersion depth ratio was changed from 0.125 to 4.0 with an increment of 0.125. Fig. 5(b) shows that the equivalent diameter of the cavitation zone rapidly increases with increasing the immersion depth ratio, and then the slope levels off as the ratio closes to 1. The reasons would be the interference of the ultrasound waves and their reflections inside the ultrasonic processing cell. The largest equivalent diameter is 2.63 cm for the immersion depth ratio of 2.0. As we move toward the right on the plot in Fig. 5(b), we can see a gradual increase in the equivalent diameter value up to d/DP = 2.0, followed by gradual reduction until d/DP = 4.0 only to be improved again until the end. Initially, the divergence of the reflected ultrasonic wave from the sidewall is limited by space. As the depth keeps increasing, there is more space available. So when the immersion depth increases, there will be multiple reflections between the ultrasonic processing cell side wall and the probe side wall resulting in different interference patterns. This can be observed in Fig. 5(b) when d/DP = 2.25. The cavitation zone extends into the narrow channel between the side wall and the probe wall. Fig. 6 shows the drastic change in cavitation zone size with a change in diameter ratio of 0.05. As the diameter ratio increases, the distance between the side walls and the source keeps increasing and at D/DP = 1.90, the constructive interference ceases thereby leading to a poor cavitation zone size. The DOE results clearly show that the diameter ratio is more significant than the immersion depth ratio. Therefore, the parametric analysis was first conducted with respect to the diameter ratio to find the appropriate value within the considered range (from 1.25 to 4.0). The results from this step show the variation of the equivalent diameter of the cavitation zone with varying diameter ratio as shown in Fig. 6. The drastic variations in the cavitation zone size
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Fig. 5. Equivalent diameter of the cavitation zone with varying (a) diameter ratio and (b) immersion depth ratio.
Table 3 Measurements of micro-hardness and surface porosity area. Sample no. 1 2
Micro hardness (HRC) 74 ± 8.7 72 ± 4.7
Surface porosity area (in.2 ) 0.077342 0.041369
From both the above analyses, the parameters of D/DP = 2.80, d/DP = 2.0 for a volume of 57 cc were identified to give the maximum cavitation zone size. 5. Experimental
Fig. 6. Cavitation zone size variation with change in diameter ratio.
Fig. 7. Cavitation zone when volume = 57 cc: (a) D/DP = 2.80, d/DP = 0.25 and (b) D/DP = 1.5, d/DP = 2.25.
can be attributed to the interference of ultrasound waves and their multiple reflections from the cell walls. It is to be noted that the diameter ratio of 2.80 gives the largest equivalent diameter, which is 2.15 cm. The increment in the cavitation size is a direct consequence of the reflection of the ultrasonic waves by the probe side walls. Initially when the d/DP is small, the cavitation zone is small and confined to the region around the probe surface (as shown in Fig. 7). We see a gradual increase in its size as the immersion depth increases. The diameter ratio is constant and so the sidewall and the probe are at a constant distance. The change is only in the depth of the probe wall. The reflections between the probe wall and the side wall can be attributed to causing this change in cavitation zone size.
An experiment was performed to study the effectiveness of ultrasonic processing using the geometric parameters determined in the computational modeling results. The experimental procedure and setup is closely followed from previously published work [25]. A master nanocomposite was prepared by Foosung Precision Industry Co., Ltd. (South Korea). It consisted of aluminum alloy A4000 (Al-11.5 Si-4.25 Cu-0.65 Mg) as the base matrix. The nanomaterials in the sample consisted of a hybrid powder comprised of carbon nanofibers (150 nm diameter, 6 m length) (CM-150, Hanwha Chemical, South Korea) and SiC micropowders (5.5 m diameter) (Greendensic GC, Showa Denko K.K, Japan). The ultrasonic source used in this experiment was a Q700 Sonicator system (Qsonica, USA). A K-type thermocouple with ceramic shielding was used to monitor the temperature of the melt. The melt zone consisted of a graphite crucible (3.6 cm diameter, 7.8 cm height), which was heated with an electric resistive heating furnace. The furnace environment was shielded with a supply of Argon gas. A schematic of the experimental setup is shown in Fig. 8. Two different samples were prepared in this experiment, by melting the Al alloy without and with ultrasonic processing. The Al alloy master nanocomposite was melted in the furnace and then poured into a stainless steel mold to prepare a disk-shaped sample (63.5 mm diameter, 12.7 mm thickness). A second sample was prepared by subjecting the Al alloy melt to ultrasonic processing with an amplitude of 60% for 15 min. The ultrasonic probe was placed inside the melt at depth of 1 (2.54 cm), following a d/Dp ratio of 2.0. The melt was then poured into the mold when the melt temperature reached 740 ◦ C. Images of the samples are shown in Fig. 8(b). A Rockwell hardness tester (hardness scale ‘C’) was used to measure the micro-hardness of the produced samples. As observed from Table 3, there was a 46% reduction in the deviation of micro hardness data in Sample 2 compared to Sample 1. This reduction indicates better homogeneous dispersion and distribution of the nanomaterials within the MMNC, due to ultrasonic processing. The surface porosity area was measured from the images of the surface of the collected samples using an image processing software, ImageJ (NIH, USA). A 50% reduction in the total
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Fig. 8. (a) Schematic of the experimental setup, (b) images of produced samples.
area of the surface pores was observed in Sample 2. In a cast part, gas porosity presents itself on the surface of the metal. So the area of the surface pores can be considered as the extent of dissolved gases present inside the sample. Ultrasonic processing can remove dissolved gases within cast parts [4]. So, the reduction in the surface pore area is an indication of the effectiveness of acoustic cavitation for material processing. 6. Conclusions A computational model was developed using the finite element method to resolve the acoustic pressure field inside the ultrasonic processing cell. Non-linear effects such as viscous losses and discontinuous boundary conditions were studied for the modeling, and the model was successfully validated using experimental results. The acoustic cavitation zones were quantitatively measured and compared with different geometric configurations of the ultrasonic processing cell. ANOVA and parametric analysis were used to investigate the dimensional effects on the acoustic cavitation involved in the ultrasonic processing. It was found that the two newly introduced parameters had significant effects on the cavitation zone size − the ratio of the ultrasonic processing cell diameter to the ultrasonic probe diameter (D/Dp ) and the ratio of the probe immersion depth to the ultrasonic probe diameter (d/Dp ). From the parametric analysis for a constant volume of 57 cc, it was observed that the ultrasonic processing cell with the geometric parameters of D/DP = 2.8 and d/DP = 2.0 provided the largest acoustic cavitation area within the studied ranges. Aluminum alloy A4000 MMNC with carbon nanofibers and SiC microparticles was used to study the effect of ultrasonic processing with decided parameters on its hardness. The sample treated by the ultrasonic processing showed a 45.98% reduction in the standard deviation of the hardness measurement and a reduction of 46.52% in total surface porosity area, which clearly shows the effect of ultrasonic processing with the determined geometric parameters on material properties. Acknowledgement The authors thank Youngsek Yang at Research Center of Foosung Precision Ind. Co., Ltd. (South Korea) for the materials used in study. References [1] Martini S. Introduction. Sonocrystallization of fats. NY: Springer New York; 2013. p. 1–5. [2] Casati R, Vedani M. Metal matrix composites reinforced by nano-particles—a review. Metals 2014;4:65–83.
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