Numerical Simulation of Ultrasonic Field During Five-Source Ultrasound-Assisted Casting of 2219 Al Alloy

Abstract

In this study, the distribution of the acoustic pressure field and cavitation threshold region in Al alloy casting under two five-source ultrasound arrangements (A and B) is investigated, aiming to optimize the five-source ultrasound configuration to improve casting quality. Numerical simulations were conducted using COMSOL software (COMSOL Multiphysics 6.0) to analyze the propagation characteristics of ultrasound in the Al melt and its influence on the cavitation effect under the two arrangements. The simulation results indicate that the cavitation threshold region for arrangement A is slightly larger than that for arrangement B. Furthermore, arrangement A demonstrates superior performance in terms of the uniformity of sound pressure distribution and the reduction in the cavitation threshold. Based on the simulation results, arrangement A was selected for experimental validation. The experimental results reveal that arrangement A, with a radial rod distance (L) of 200 mm from the center point and an insertion depth (H) of 270 mm, significantly refines the grains and improves the distribution of the second phase, thereby confirming the reliability of the simulation results. This study provides a theoretical foundation and practical guidance for the application of five-source ultrasound in Al alloy casting.

1. Introduction

2219 Al alloy has been widely used in aerospace, automotive manufacturing, the electronics industry, and other fields due to its excellent mechanical properties, corrosion resistance, and lightweight characteristics [1,2,3,4,5,6,7,8]. However, the traditional casting process of Al alloys often faces challenges such as coarse grain size, porosity, shrinkage, and other, which significantly impair the mechanical properties and service life of castings [9,10,11,12,13]. To address these issues, ultrasonic-assisted casting technology has gained considerable attention in recent years as an innovative casting method [14,15,16,17,18,19,20,21].

In recent years, scholars worldwide have conducted extensive research on ultrasonic-assisted casting technology [22,23,24,25,26]. For instance, Eskin et al. [27] investigated the propagation behavior of ultrasonic waves in Al alloy melts and found that ultrasonic treatment significantly refines grain size and reduces defects such as porosity and shrinkage. Zhang et al. [16] studied the acoustic pressure distribution and acoustic flow effects of ultrasonic waves in Al alloy melts using a combination of experiments and numerical simulations. Their findings revealed that ultrasonic waves promote melt convection and homogenize solute distribution. Zhang et al. [28] explored Four-source ultrasonic-assisted casting technology and demonstrated that multi-source ultrasonic waves further enhance the uniformity of ultrasonic energy distribution in the melt, thereby improving casting quality more effectively. Fang et al. [29] investigated the distribution patterns of acoustic and flow fields during multi-source ultrasonic melt processing. Results indicate that during four-source ultrasonic treatment, the effective cavitation zone within the melt significantly expanded, demonstrating pronounced cavitation effects. Zhang et al. [30] investigated the effect of phase difference in dual-source ultrasonic-assisted casting on grain refinement in Al alloys. Under identical vibration frequencies, the phase difference exerted negligible influence on grain refinement at the casting edge and within the ultrasonic radiation zone. Under varying vibration frequencies, the phase difference had no discernible impact on grain refinement within the ingot.

The integration of ultrasonic cavitation measurement, cavitation meters, and high-temperature acoustic sensing holds significant importance for understanding and optimising various ultrasonic processes. For instance, in the ultrasonic treatment of molten metals, high-temperature cavitation meters can provide critical data to optimise acoustic power levels and temperature ranges [31,32]. However, sensor reliability, stability, and accuracy remain significant challenges in extreme environments characterised by high temperatures, high pressures, and strong corrosion [33,34]. Tzanakis et al. [35] employed a calibrated high-temperature cavitometer to measure acoustic emissions and sound pressure levels in ultrasonically treated liquid Al and water. The extent of cavitation zones within the liquid Al and water was quantified.

Multi-source ultrasonic-assisted casting technology builds upon single-source ultrasonic systems by employing multiple ultrasonic sources simultaneously. This approach enhances the uniformity of ultrasonic energy distribution within the melt, thereby improving casting quality more effectively [28]. As a variant of multi-source ultrasonic technology, five-source ultrasonic-assisted casting technology offers higher energy density and more uniform energy distribution, making it a promising method for Al alloy casting. However, optimizing process parameters and understanding the underlying mechanisms of five-source ultrasonic-assisted Al alloy casting remain significant challenges. Due to experimental limitations, directly studying the propagation behavior of ultrasonic waves in the melt and their influence on the solidification process is difficult [36,37]. Consequently, numerical simulation has become a widely used tool in ultrasonic-assisted casting research. Through numerical simulation, the propagation characteristics of ultrasonic waves in the melt can be visualized, their impact on the solidification process can be analyzed, and process parameters can be optimized [38,39,40].

This study aims to investigate the propagation behavior of five-source ultrasonic waves in Al alloy casting and their influence on the solidification process using numerical simulation. First, a numerical model of five-source ultrasonic-assisted Al alloy casting is established based on acoustic theory and fluid dynamics principles. Next, the distribution of the acoustic pressure field and the cavitation threshold region in the melt is analyzed through numerical simulation to explore the effects of different five-source ultrasound arrangements on the Al melt. Finally, by comparing numerical simulation results under varying process parameters, the process parameters for five-source ultrasonic-assisted Al alloy casting are optimized, providing theoretical guidance for practical applications.

2. Numerical Simulation

2.1. Geometrical Model Parameters

The strength of the acoustic field directly influences the organizational improvement of the metal melt. The size of the cavitation threshold region and the cavitation intensity within this region significantly affect the cavitation mechanism. Additionally, the directivity of the acoustic field, determined by the arrangement of ultrasonic sources, impacts the macroscopic homogeneity of the metal’s microstructure. Therefore, this paper focuses on a centrally symmetric homogeneous arrangement. After analysis, two primary types of arrangements are identified. For clarity, these arrangements are defined as Type A and Type B, respectively, and their schematic diagrams are illustrated in Figure 1.

First, a three-dimensional geometric model is established using COMSOL software (COMSOL Multiphysics 6.0). The model is axisymmetric, and to simplify the calculations, only half of the model is constructed, as illustrated in Figure 2. The geometric model represents a melt space with a height of 1050 mm and a radius of 625 mm. The physical parameters of the material are provided in

Table 1. Numerical simulation of material process parameters.

Parameters	Values
Density	2700 $\mathrm{kg}·{\mathrm{m}}^{-3}$
Liquid phase line temperature	916 K
Solid phase line temperature	816 K
Specific heat	864 $\mathrm{J}·{\left(\mathrm{kg}·\mathrm{K}\right)}^{-1}$
Latent heat of crystallization	360,000 $\mathrm{J}·{\mathrm{kg}}^{-1}$
Velocity of sound in Al melt	2600 $\mathrm{m}·{\mathrm{s}}^{-1}$
Velocity of sound in air	341 $\mathrm{m}·{\mathrm{s}}^{-1}$

.

The model developed in this paper incorporates two variables: the insertion depth of the radial rods into the free liquid surface, denoted as H, and the distance of each radial rod from the center point, denoted as L, as illustrated in Figure 3.

2.2. Numerical Calculation of Single-Source Ultrasonic Fields

For high-energy ultrasonic vibration systems equipped with long radiating rods, it is essential to measure the acoustic pressure distribution at the end faces of these radiating rods. Subsequently, theories of acoustic impedance and acoustic transmission can be utilized to analyze the radiated acoustic pressure in the surrounding fluid. It is known that only longitudinal waves exist in the fluid medium, and the acoustic field is characterized by acoustic pressure. This pressure can be effectively determined within its cavitation threshold region. Furthermore, the classical acoustic pressure distribution equation can be derived from the Helmholtz equation [41,42], which can be expressed as follows:

$$p_0=j\omega {\displaystyle \frac{\rho u_a{R}^2}{2r}}\left[{\displaystyle \frac{2J_1\left(kRsin\theta \right)}{kRsin\theta }}\right]e^{j\left(\omega t-kr\right)}$$

(1)

Taking only the amplitude part of its sound pressure:

$$p_0={\displaystyle \frac{\rho u_a\omega R^2}{2r}}\left[{\displaystyle \frac{2J_1\left(kRsin\theta \right)}{kRsin\theta }}\right]$$

(2)

where $\rho$ denotes the medium density, $u_a$ denotes the plasmonic amplitude, $\omega$ denotes the angular velocity, $R$ denotes the radius of the ultrasonic probe end face, and $k$ denotes the wave number. Combine the sound pressure $p_a$ with the medium amplitude $u_a$ [43,44]:

$$p_a=\rho c{u}_a$$

(3)

After simple arithmetic, the formula for the sound pressure distribution in the spherical coordinate system can be obtained:

$$p_0={\displaystyle \frac{p_a{F}_s}{\lambda r}}·{\displaystyle \frac{2J_1\left(kRsin\theta \right)}{kRsin\theta }}$$

(4)

2.3. Numerical Calculation of Five-Source Ultrasonic Fields

To examine the sound pressure distribution along the acoustic axis cross-section in greater detail, classical Bessel’s equation is employed to directly describe the distribution of the five-source ultrasonic field, as well as its attenuation process in three-dimensional space. From the sound pressure distribution of single-rod ultrasonic systems, it can be deduced that the radiated sound pressures of each of the five variable-amplitude rods in the Cartesian coordinate system can be represented in spherical coordinates as follows:

$$p_1={\displaystyle \frac{p_a{F}_s}{\lambda r_1}}·{\displaystyle \frac{2J_1\left(kRsin{\theta }_1\right)}{kRsin{\theta }_1}}$$

(5)

$$p_2={\displaystyle \frac{p_a{F}_s}{\lambda r_2}}·{\displaystyle \frac{2J_1\left(kRsin{\theta }_2\right)}{kRsin{\theta }_2}}$$

(6)

$$p_3={\displaystyle \frac{p_a{F}_s}{\lambda r_3}}·{\displaystyle \frac{2J_1\left(kRsin{\theta }_3\right)}{kRsin{\theta }_3}}$$

(7)

$$p_4={\displaystyle \frac{p_a{F}_s}{\lambda r_4}}·{\displaystyle \frac{2J_1\left(kRsin{\theta }_4\right)}{kRsin{\theta }_4}}$$

(8)

$$p_5={\displaystyle \frac{p_a{F}_s}{\lambda r_5}}·{\displaystyle \frac{2J_1\left(kRsin{\theta }_5\right)}{kRsin{\theta }_5}}$$

(9)

Included among these is

$$F_s=\pi R^2$$

(10)

Translating the factors $r$ and $\theta$ therein into a Cartesian coordinate system results in:

$$r_1=\sqrt{{\left(0.2-z\right)}^2+x^2+y^2}$$

(11)

$$r_2=\sqrt{{\left(x+0.2\times cos{\displaystyle \frac{\pi }{10}}\right)}^2+{\left(0.2\times sin{\displaystyle \frac{\pi }{10}}-z\right)}^2+y^2}$$

(12)

$$r_3=\sqrt{{\left(x-0.2\times cos{\displaystyle \frac{\pi }{10}}\right)}^2+{\left(0.2\times sin{\displaystyle \frac{\pi }{10}}-z\right)}^2+y^2}$$

(13)

$$r_4=\sqrt{{\left(x-0.2\times cos{\displaystyle \frac{\pi }{5}}\right)}^2+{\left(0.2\times sin{\displaystyle \frac{\pi }{5}}+z\right)}^2+y^2}$$

(14)

$$r_5=\sqrt{{\left(x+0.2\times cos{\displaystyle \frac{\pi }{5}}\right)}^2+{\left(0.2\times sin{\displaystyle \frac{\pi }{5}}+z\right)}^2+y^2}$$

(15)

Included among these are

$$sin{\theta }_1={\displaystyle \frac{\sqrt{{r_1}^2-y^2}}{{r_1}^2}}$$

(16)

$$sin{\theta }_2={\displaystyle \frac{\sqrt{{r_2}^2-y^2}}{{r_2}^2}}$$

(17)

$$sin{\theta }_3={\displaystyle \frac{\sqrt{{r_3}^2-y^2}}{{r_3}^2}}$$

(18)

$$sin{\theta }_4={\displaystyle \frac{\sqrt{{r_4}^2-y^2}}{{r_4}^2}}$$

(19)

$$sin{\theta }_5={\displaystyle \frac{\sqrt{{r_5}^2-y^2}}{{r_5}^2}}$$

(20)

According to the superposition principle of linear acoustics, the total sound pressure value $p_{all}$ radiated by the five sources of ultrasound can be obtained as follows:

$$p_{all}=p_1+p_2+p_3+p_4+p_5$$

(21)

The ultrasonic radiation rod, when immersed in water and subjected to vibration, allows for the calculation of the sound pressure distribution contour at the end face of the amplifier rod using MATLAB software (Matlab 2024a). This enables the determination of the sound pressure distribution at the end face of a single-rod transducer operating in water, as illustrated in Figure 4.

From Figure 4, it can be observed that the sound pressure values influencing the sound power primarily fall within the range of 0.001 m to 0.005 m from the center of the radial rod end face. Therefore, the sound pressure values at five points are equivalently collected in this region. The simulation results presented in Figure 4 indicate that the sound pressure values between 0.005 m and 0.025 m are relatively low, with minimal variation in sound pressure values ranging from 0.015 m to 0.025 m compared to those in the 0.005 m range; thus, the sound pressure value at 0.015 m is taken uniformly.

Similarly, three points are selected in the range of 0.006 m to 0.015 m. Due to the limitations of simulation accuracy, we cannot ensure that these points are located on the isotropic surface. Consequently, points are chosen based on proximity to the isotropic surface, specifically at 0.007 m, 0.010 m, and 0.015 m. This results in a total of nine sound pressure values being recorded. The sound pressure values at each point are summarized in

Table 2. Parameters required for five-source ultrasound-assisted casting simulation.

Y/mm	Sound Pressure/Pa	Y/mm	Sound Pressure/Pa
1	$1.3\times {10}^8$	7	$1.9\times {10}^7$
2	$6.5\times {10}^7$	10	$1.3\times {10}^7$
3	$4.3\times {10}^7$	15	$8.6\times {10}^6$
4	$3.2\times {10}^7$	25	$5.2\times {10}^6$
5	$2.6\times {10}^7$

.

2.4. Boundary Condition Setting

In the COMSOL model, the Pressure Acoustics Module was employed with a time-harmonic study type, utilising COMSOL’s default frequency-domain solver. In this study, the ultrasonic transducer employs electroacoustic conversion to transmit energy to the end face of the radiator rod, from which it is introduced into the aluminium melt. Upon entering the aluminium melt, the acoustic energy undergoes scattering and attenuation, whilst encountering various boundaries it undergoes phenomena such as refraction. The physical model for acoustic energy transmission is illustrated in Figure 5.

The red arrows in Figure 5 indicate the direction of sound energy transmission. After sound energy is introduced into the aluminium melt via the end face of the radiator rod, five interfaces affect its transmission: the free liquid surface, the inner wall of the hot top, the inner wall of the mould, the side wall of the radiator rod, and the liquid pocket.

The impedance $R_l$ of the molten aluminium is

$$R_l={\rho }_l{c}_l$$

(22)

This study adopts the density ${\rho }_l$ of aluminium alloy 2219 as 2700 kg/m³, and the sound velocity $c_l$ as 2600 m/s. Substituting these values into the formula yields the impedance of the molten aluminium. Similarly, the impedances for air, the inner wall of the hot top, the inner wall of the mould, and the side wall of the radiator rod can be obtained. The liquid pocket is treated separately as a porous medium. The boundaries are defined as follows:

Free liquid surface. The acoustic boundary properties here constitute a soft boundary, where $R_l\gg R_a$ at this interface, with $R_a$

(1)

being the impedance in air. When ultrasound propagates from the source to this interface, the acoustic energy undergoes total reflection back into the aluminium melt, causing the fluid at the melt surface to enter a state of tensile stress.

(2)

Inner wall of the hot top. The acoustic boundary here is partially sound-transmissive. At this interface, the acoustic energy of ultrasonic waves transmitted from the molten aluminium through the hot top wall is determined by the following equation:

$${\displaystyle \frac{p_t}{p_l}}={\displaystyle \frac{2R_t}{R_l+R_t}}$$

(23)

The proton velocity loss may be determined by Equation (24).

$${\displaystyle \frac{v_t}{v_l}}={\displaystyle \frac{2R_l}{R_l+R_t}}$$

(24)

$p_t$ denotes the sound pressure transmitted into the wall surface of the ceramic silicon carbide hot top, $p_l$ represents the sound pressure within the aluminium alloy, $R_t$ signifies the acoustic impedance of the ceramic silicon carbide, $v_t$ indicates the vibration velocity of the ceramic silicon carbide phonons at the hot top wall surface, and $v_l$ denotes the vibration velocity of the aluminium alloy melt phonons.

(3)

Inner wall of the crystalliser. The majority of the crystalliser’s inner wall surface consists of graphite rings, where the interface between the aluminium alloy melt and the graphite material is considered to be the boundary. The acoustic energy transmitted through this interface from the aluminium melt, as determined by the sound pressure across the crystalliser’s inner wall, is defined by the following equation:

$${\displaystyle \frac{p_s}{p_l}}={\displaystyle \frac{2R_s}{R_l+R_s}}$$

(25)

The loss of proton velocity may be determined by the following equation:

$${\displaystyle \frac{v_s}{v_l}}={\displaystyle \frac{2R_l}{R_l+R_s}}$$

(26)

where $p_s$ denotes the sound pressure transmitted into the graphite material, $R_s$ represents the acoustic impedance of the graphite material, and $v_s$ signifies the vibration velocity of graphite protons within the graphite material.

(4)

Radiation rod side wall. Here, $R_l\ll R_t$ is considered a hard boundary surface. When acoustic energy is transmitted from the source to this interface, it is assumed that all sound energy is reflected back into the aluminium melt, with the fluid at the interface being in a compressed state.

2.5. Mesh Sensitivity Analysis

Second-order Lagrange tetrahedral elements were used throughout the computational domain. This element type provides a good balance between computational accuracy and cost for acoustic wave propagation problems. A physics-controlled mesh sequence was employed. Local refinements were applied to the critical regions: (1) The regions immediately surrounding the five ultrasonic sonotrodes. (2) The anticipated high-pressure zones and acoustic interaction regions in the melt pool. This strategy ensures high solution accuracy where the acoustic field gradients are steepest while maintaining computational efficiency in larger volumes of the domain where changes are more gradual.

The final mesh for the primary simulation domain consisted of approximately 1.45 million elements. The maximum element size in the bulk fluid domain was 20 mm, and the minimum element size in the refined zones near the sonotrodes was 5 mm. The model had approximately 2.1 million degrees of freedom.

The pressure acoustics, frequency domain interface in COMSOL was solved using the Stationary (Frequency Domain) study type. The fully coupled linear system was solved using the MUMPS (MUltifrontal Massively Parallel sparse direct Solver) algorithm. The relative tolerance was set to 1.0 × 10⁻⁶ and the absolute tolerance was set to 1.0 × 10⁻⁹, which are the default stringent tolerance settings in COMSOL for ensuring convergence of the acoustic field solution.

This study was performed on the A-arrangement model with parameters L = 200 mm and H = 270 mm (the optimal configuration identified in our study). We tested four different mesh sizes, ranging from “Coarser” to “Finer”, by adjusting the global element size scaling factor in COMSOL. The key output parameters monitored were Maximum Acoustic Pressure, Cavitation Depth and Cavitation Percentage. The results of the mesh sensitivity analysis are summarized in

Table 3. Results of the mesh independence study for the A-arrangement model (L = 200 mm, H = 270 mm).

Mesh Setting	Element Size Range (mm)	Total Number of Elements	Maximum Acoustic Pressure (MPa)	Cavitation Depth (mm)	Cavitation Percentage (%)
Extremely Coarse	40–80	25,000	2.85	320	2.15
Coarser	20–40	85,000	3.12	345	2.38
Normal	10–20	350,000	3.21	358	2.49
Finer	5–10	1,450,000	3.24	360	2.50
Extra Fine	2.5–5	5,800,000	3.25	361	2.51

.

As demonstrated in Table 3, the key output parameters (Acoustic Pressure, Cavitation Depth and Cavitation Percentage) converge as the mesh is refined. The results show a negligible change (less than 1% for Acoustic Pressure and Cavitation Depth, and less than 0.5% for Cavitation Percentage) when the mesh is refined from the “Finer” setting to the “Extra Fine” setting. This confirms that the solution has achieved mesh independence at the “Finer” setting. Therefore, the “Finer” mesh (with approximately 1.45 million elements) was selected for all production simulations presented in the paper, as it provides an optimal balance between computational accuracy and cost.

3. Results and Discussion

3.1. Numerical Simulation Results for Arrangement A

In the A arrangement, when the insertion depth H is set to 100 mm, 200 mm, and 300 mm, the distribution of the acoustic pressure field, the acoustic pressure isosurface, and the cavitation threshold region within the melt can be analyzed by varying the distance L of each radiating rod from the center point.

Typical simulation results were obtained by adjusting the distance L of each radiating rod from the center point for H = 100, 200, 300 mm, as illustrated in Figure 6, Figure 7 and Figure 8. The left side of each figure displays the acoustic pressure field, the middle shows the acoustic pressure equivalent surface, and the right side depicts the cavitation threshold region. Comparing Figure 6a,e, it can be seen that when the insertion depth H of the radial rods is certain, the cavitation threshold region increases slightly with the increase in the distance from the five radial rods to the centre. On the contrary, comparing Figure 6, Figure 7 and Figure 8, it can be seen that when the insertion depth H is increasing from 100 mm to 300 mm, the cavitation threshold shows a decreasing trend.

Typical simulation results are presented in Figure 9, Figure 10 and Figure 11, which illustrate the effects of varying the insertion depth H of the radiating rods for distances L = 100, 150, and 200 mm in the A arrangement mode. Comparing Figure 9a,e indicates that the cavitation threshold region decreases continuously as the insertion depth H increases, while the distance L from the center point of each radiating rod remains constant. Conversely, a comparison of Figure 9, Figure 10 and Figure 11, reveals that as the distance L of each radial rod from the center point increases from 100 mm to 200 mm, the cavitation threshold appears to increase.

3.2. Numerical Simulation Results for Arrangement B

Typical simulation results are presented in Figure 12, Figure 13 and Figure 14, which illustrate the effects of varying the distance L of each radiating rod from the center point for insertion depths H = 100, 200, and 300 mm in the B arrangement mode. Comparing Figure 12a with e, it is evident that when the insertion depth H of the radiating rods is held constant, the cavitation threshold region increases slightly as the distance from the center of the five radiating rods increases. Conversely, a comparison of Figure 12, Figure 13 and Figure 14 shows that as the insertion depth H increases from 100 mm to 300 mm, the cavitation threshold appears to decrease. This trend is consistent with the results observed in the A arrangement mode.

In the B arrangement mode, typical simulation results are illustrated in Figure 15, Figure 16 and Figure 17, which show the effects of varying the insertion depth H of the radiating rods for distances L = 100, 150, and 200 mm.

Comparing Figure 15a with e, it is evident that the cavitation threshold region decreases continuously as the insertion depth H increases while maintaining a constant distance L from the center point of each radiating rod. Conversely, a comparison of Figure 15, Figure 16 and Figure 17 reveals that as the distance L of each radial rod from the center point increases from 100 mm to 200 mm, the cavitation threshold appears to increase. This trend is consistent with the results observed in the A arrangement mode.

3.3. Impact of Placement on the Cavitation Threshold Region

The total number of grids, the number of cavitation threshold grids and the deepest point of the cavitation threshold for each model were analysed and collated, and each quantity is briefly described below:

(1)

Total number of grids: the number of all grids obtained by meshing before the model is calculated.

(2)

Cavitation Threshold Grids: The number of grids with sound pressure values higher than 1.1 MPa in the calculation results extracted after post-processing, referred to as “Cavitation Grids”.

(3)

Cavitation threshold depth: After post-processing, the grid with the largest distance from the free liquid surface along the plumb direction of the grid with the cavitation threshold is obtained, and the distance from the grid to the free liquid surface is recorded, which is referred to as the “cavitation depth”.

(4)

Cavitation threshold as a percentage of all grids: It is used to measure the influence of the arrangement on the size of the cavitation threshold area, i.e., the quotient of the number of grids with the cavitation threshold and the total number of grids, referred to as the ‘percentage of cavitation’, calculated as follows:

$$\mathrm{Percentage}\mathrm{of} \mathrm{cavitation}={\displaystyle \frac{\mathrm{Number} \mathrm{of} \mathrm{cavitation} \mathrm{threshold} \mathrm{grids}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{meshes} \mathrm{in} \mathrm{the} \mathrm{model}}}\times 100\%$$

(27)

In order to compare more intuitively the effect of the insertion depth H value and the distance L value from the centre point of each radial rod on the melt cavitation threshold, the variation curves of the cavitation depth and the cavitation percentage for the A arrangement and the B arrangement are shown in Figure 18.

From Figure 18a, it can be observed that when the insertion depth H is held constant, the cavitation depth is larger with smaller distances L of each radial rod from the center point. As the distance L increases, the cavitation depth exhibits a decreasing trend. This phenomenon occurs because, at a constant insertion depth H, a smaller value of L exerts a stronger enhancement effect in the central part of the aluminum melt, resulting in greater acoustic energy convergence in the middle region. Consequently, this allows for a larger depth to be reached within the cavitation threshold region. Conversely, as L increases, the convergence effect diminishes, leading to a decrease in the attainable depth within the cavitation threshold region.

In Figure 18a, the maximum cavitation depth reaches 380 mm below the free liquid surface when H is 100 mm and L is 100 mm. In contrast, the minimum cavitation depth recorded is 300 mm when H is 100 mm and L is 270 mm in the A arrangement mode. Furthermore, Figure 18b illustrates that the cavitation depth is larger when the insertion depth H is increased while keeping the distance L between each radial rod and the center point constant. As H increases, the cavitation depth demonstrates an increasing trend.

From Figure 18c, it can be observed that when the insertion depth H is held constant, a larger value of L results in an increased cavitation threshold region when H is set to 100 mm. However, if L becomes excessively large, the depth of the cavitation threshold region diminishes, which may hinder the improvement of the metal structure at the solidification front. For insertion depths of H = 200 mm and H = 300 mm, changes in the value of L have minimal impact on the size of the cavitation threshold region. This is attributed to the significant superposition effect occurring in the cavitation region of individual radial rods when H is fixed. Although there is a stronger convergence effect in the middle region of the aluminum melt, the proximity of the radial rods, along with the influence of other sound sources, can enhance the cavitation intensity around each individual radial rod. Nevertheless, this results in a reduction in the overall range of the cavitation threshold region.

By comparison, it can be noted that the cavitation threshold area for arrangement A is slightly larger than that for arrangement B. In arrangement A, when H is 100 mm and L is 100 mm, the percentage of the cavitation threshold is the smallest at 8.78%. Conversely, when L is 270 mm, the percentage of the cavitation threshold increases to its largest value of 15.16%.

As illustrated in Figure 18d, when the value of L is held constant, the percentage of cavitation decreases as the insertion depth H increases. Specifically, when L is set to 100 mm, variations in H have minimal effect on the depth of the cavitation threshold. However, for values of L at 150 mm and 200 mm, an increase in H results in a greater depth of the cavitation threshold region, which is beneficial for improving the metal structure.

After comparison within the discussed parameter range, the A arrangement is identified as optimal, with a distance L of 200 mm and an insertion depth H of 270 mm. This configuration yields a cavitation depth of 360 mm and a percentage of the cavitation threshold region of 2.50%, along with a small sound pressure gradient in its sound pressure field. The corresponding sound pressure isosurface is schematically depicted in Figure 19.

Five-source ultrasonic-assisted casting was conducted using the A arrangement, with the insertion depth of the radiating rod set to H = 270 mm and the distance from the radiating rod to the center axis of the aluminum melt set at L = 200 mm.

The experimental material employed in this study is 2219 Al alloy, the primary chemical composition of which is presented in

Table 4. Main components of 2219 Al alloy (wt.%) [45].

Cu	Mn	Zr	V	Fe	Si	Mg	Zn	Ti	Al
6.20	0.36	0.11	0.1	0.1	0.06	0.01	0.10	0.05	Bal.

. Typical metallographic microstructures of 2219 Al alloy ingots at different locations are shown in Figure 20. The average grain sizes at different locations are summarised in Figure 21. Without ultrasonic treatment (UST), the average grain sizes in the center, half radius, and edge regions were 446, 305, and 218 μm, respectively. Following ultrasonic treatment, the average grain sizes in the center, half radius, and edge regions were 382, 284, and 189 μm, respectively, representing refinements of 14.3%, 6.9%, and 13.3% compared to the untreated samples.

The typical scanning electron microscopy (SEM) microstructures of different regions of 2219 Al alloy ingots are presented in Figure 22. In the A arrangement mode, the coarse Al₂Cu second phase microstructure is significantly reduced, and the diffuse distribution effect is enhanced compared to the ingot without ultrasonic treatment. Figure 22d–f, illustrate that the distribution of the second phase becomes finer and more uniform.

For a more intuitive observation, the area fraction of the second phase was quantified using Image Pro Plus software (Image Pro Plus 6.0), with results displayed in Figure 23. When five sources of ultrasound are applied to the aluminum melt in the A arrangement, the second phase area fractions are consistently smaller than those of the ingot without ultrasonic treatment. Notably, the area fraction of Al₂Cu decreases substantially, reaching a minimum value of 5.9%. This arrangement creates a significant superposition effect in the cavitation area produced by the ultrasound, maximizing the ultrasonic effect to refine the distribution of the second phase, which aligns with the simulation results.

The tensile mechanical properties of 2219 Al alloy ingot samples at different locations are shown in Figure 24. Without ultrasonic treatment, the ultimate tensile strength (UTS), yield strength (YS) and elongation (EI) were 184.6 MPa, 75.6 MPa and 4.3%, respectively. With ultrasonic treatment, the UTS, YS, and EI were 196.2 MPa, 80.8 MPa, and 4.8%, respectively, representing increases of 6.3%, 6.9%, and 11.6%. This demonstrates that applying five-source ultrasonic treatment effectively enhances the mechanical properties of the ingot.

4. Conclusions

In this paper, the simulation of five-source ultrasonic field is carried out using COMSOL software to obtain the distribution of acoustic pressure field, acoustic pressure iso-surface and cavitation threshold region in Al melt under two different arrangements. The depth of cavitation and the percentage of cavitation under different arrangements were analysed and compared. The following conclusions were obtained:

(1)

When the insertion depth H is certain, the cavitation depth is larger when the distance L of each radiating rod from the centre point is small. As the distance L increases, the cavitation depth shows a decreasing trend. In the A arrangement mode, when H is 100 and L is 100 mm, the cavitation depth is the largest and can reach 380 mm below the free liquid surface; when H is 100 and L is 270 mm, the cavitation depth is the smallest and is 300 mm.

(2)

When the value of insertion depth H is certain, i.e., when the value of insertion depth H is 100 mm, the larger the value of L is, the larger the cavitation threshold area is, but if the value of L is too large, at this time, the depth of the cavitation threshold area is small, which is detrimental to the improvement of the metal tissue along the solidification front. In the A arrangement, when H is 100 mm, L is 100 mm, and the percentage of the cavitation threshold is the smallest, which is 8.78%; when the value of L is 270 mm, the percentage of cavitation threshold is maximum at 15.16%.

(3)

When the value of L is certain, the percentage of cavitation decreases as the insertion depth H increases. When the value of L is 100 mm, changing the value of H has little effect on the depth of the cavitation threshold, and when the value of L is 150 mm and 200 mm, the increase in the value of H increases the depth of the cavitation threshold region, which is conducive to the improvement of the metal tissue.

(4)

Within the parameter range discussed in this paper, the optimal process parameters are selected as the A arrangement, the distance L is 200 mm, the insertion depth H is 270 mm as the optimal arrangement, the cavitation depth is 360 mm, the percentage of the cavitation threshold region is 2.50%, and the sound pressure gradient in its sound pressure field is small.