Effect of the arrangement of cavitation generation unit on the performance of an advanced rotational hydrodynamic cavitation reactor

Highlights

• •Effects of CGU arrangement on ARHCR performance are studied by CFD.
• •The “simplified flow field” strategy was utilized.
• •Lower intersection angle and number of rows are benefit to performance.
• •Proper radial and circumferential offsets and radial spacing are advisable.
• •This work may provide a reference value to the design of ARHCRs.

Abstract

Hydrodynamic cavitation (HC) is widely considered a promising process intensification technology. The novel advanced rotational hydrodynamic cavitation reactors (ARHCRs), with considerably higher performance compared with traditional devices, have gained increasing attention of academic and industrial communities. The cavitation generation unit (CGU), located on the rotor and/or stator of an ARHCR, is utilized to generate cavitation and consequently, its geometrical structure is vital for the performance. The present work studied, for the first time, the effect of the arrangement of CGU on the performance of a representative ARHCR by employing computational fluid dynamics based on the “simplified flow field” strategy. The effect of CGU arrangement, which was neglected in the past, was evaluated: radial offset distance (c), intersection angle (ω), number of rows (N), circumferential offset angle (γ), and radial spacing (r). The results indicate that the CGU, with an arrangement of a low ω and moderate c, N, γ, and r, performed the highest cavitation efficiency. The corresponding reasons were analyzed by combining the flow field and cavitation pattern. Moreover, the results also exposed a weakness of the “simplified flow field” strategy which may induce the unfavorable “sidewall effect” and cause false high-pressure region. The findings of this work may provide a reference value to the design of ARHCRs.

1. Introduction

Process intensification (PI), which was firstly conceptualized by Imperial Chemical Industries (ICI) in the late 1970 s, aims to make chemical processes substantially smaller, cleaner, safer, and cheaper by employing novel reactors and methods, e.g., multifunctional reactors, hybrid separations, alternative energy sources, and others [1]. PI has become a promising pathway for enhancing the sustainability and economics of chemical industry, especially under the global background of carbon neutrality. As a novel alternative energy source method, hydrodynamic cavitation (HC) is widely considered a prospective PI technology, as several advantages of low operational and equipment costs, mild reaction conditions, and most importantly, high scalability, compared with other energy sources such as ultrasound, microwave, and electric field [2], [3], [4]. HC phenomenon, discovered by Euler [5] in water wheels as early as in 1756, is a rapid phase-change phenomenon, including formation, growth, and collapse, triggered by local pressure change [6], [7], and releases tremendous energy into surrounding liquids, creating unique reaction environment with local high pressures and temperatures and strong oxidation/reduction effects [8], [9], [10]. The sonochemical effect induced by HC has been widely investigated and applied in various chemical and environmental applications in the past 30 years: degradation of organic matter [11], disinfection [12], disintegration of waste activated sludge [13], emulsification (including biodiesel synthesis) [14], delignification [15], food processing [16], flotation [17], surface finishing and washing [18], denitration [19], heat generation [20], etc.

HC is intentionally produced by a hydrodynamic cavitation reactor (HCR), therefore, its structure generally determines the cavitation intensity and consequent treatment effectiveness of HC technology, indicating the importance of designing high-performance HCRs [28], [29], [30]. Recently, the advanced rotational HCRs (ARHCRs), which possess different structures and generation mechanisms from the popular conventional HCRs (e.g., Venturi, orifice, and vortex diode), have attracted increasing attention from the academic and industrial communities, due to high treatment effectiveness and process rate [31], [32]. Some ARHCRs with fine design can be operated in a continuous mode for biodiesel production [23], [33], [34], microbial inactivation of milk [35], [36], and pretreatment of lignocellulose biomass (e.g., commercialized products from BioBANG company), demonstrating great potential for industrial-scale applications. In general, an ARHCR utilizes bulges or holes with various shapes located on the rotor (so-called cavitation generation unit, CGU) to periodically generate cavitation. In terms of rotor geometry, the ARHCR can be divided into the disk type and the cylinder type; and according to whether there are CGUs located on the stator, it can be classified into the shear type (Fig. 1 (a)) and the interactiontype (Fig. 1 (b)) [37], [38]. The interaction type normally shows greater treatment effectiveness compared with the shear type, because the interaction between the rotor and stator not only enhances cavitation generation by increasing the relative velocity between the liquid and rotor, but also considerably raises the frequency of generation and collapse, as confirmed in our previous works [39]. The detailed operational mechanism of these two types of reactors can be found in many reviews [40], [41], [42].

Fig. 1.

Representative ARHCRs: (a) shear type [21], [22], [23] and (b) interaction type [24], [25], [26], [27].

Compared with application research, the research on interaction-type reactors themself is still very limited. A few researchers attempted to preliminarily explore their flow mechanisms, by utilizing experimental flow visualization [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], computational fluid dynamics (CFD) [38], [53], [54], and external characteristic experiment [43], [44], [45], [46], [47], [49], [51], [52] in the past few years. Regarding the effect of reactor structure on performance, we demonstrated, for the first time, the influence of CGU structure of a disk reactor (i.e., shape, diameter, interaction distance, height, and inclination angle [39]) by CFD; and optimized the last four factors by combining CFD and genetic algorithm in a following work [55]. Then, Song, et al. [38] and Zhang, et al. [56] investigated the effects of CGU shape and distance and the effects of diameter, height, and cone bottom length of CGU, respectively. Apart from CGU structure, the arrangement of CGU, e.g., the spacing between each CGU, number of rows, or relative position of CGUs, is also worth considering. Even though ARHCRs with various arrangements of CGUs have been widely manufactured and employed (Fig. 1), the study relating to the influence of CGU arrangement has not been conducted in the past to the best of our knowledge, which could restrict the application and development of ARHCR-based HC technology.

To this, we herein provide a numerical simulation of the effect of CGU arrangement on the performance of an interaction, disk-type ARHCR (Fig. 2 (a)) [25], [36], [47], [57] by utilizing the “simplified flow field” CFD strategy validated in our previous works [39], [53], [55], [58]. The effects of four important factors of CGUs, which were rarely considered in the previous studies, on the amount of cavitation generation and generation efficiency were evaluated: the radial offset distance of a pair of moving and static CGUs; the intersection angle between each CGU in one row (which stands for the number of CGUs in one row); the radial spacing and circumferential offset angle between each row; and the number of rows. The reasons leading to the difference in performance were elucidated by analyzing the corresponding flow and pressure fields. The relevant findings could provide an effective reference for the fundamental understanding and design of interaction-type ARHCRs for process intensification.

Fig. 2.

Schematic diagram of the ARHCR (a) and the computational domain of the simplified interaction region (b) [39], [53], [55].

2. Numerical method

2.1. “Simplified flow field” CFD strategy

Since the numerical simulation on the full flow field of the ARHCR with numerous CGUs often requires high spatial and temporal resolutions and massive computation resources, it is necessary to properly simplify the full flow field in terms of the flow characteristics. To achieve this purpose, we proposed a “simplified flow field” CFD strategy in the past [39], [53], [55] which simplifies the full model into 1/n of the interaction region as it is rotationally symmetrical, as shown in Fig. 2. In the present work, n is 32 as the number of the CGUs on the rotor of the reactor is 32. The commercial CFD code ANSYS Fluent 18.2 was employed to predict the flow field and performance of the ARHCR by combining the shear stress transport k-omega model and Schnerr-Sauer model, as turbulence model and cavitation model, respectively. By applying periodic conditions on both the moving part and the static part with dynamic mesh method (Fig. 2 (b)), the interaction motion of the CGUs located on the stator and rotor can be obtained, which induces sheet cavitation (SC) and vortex cavitation (VC) on the downstream side of CGUs and inside the CGUs, respectively. Although this strategy underestimates the development and evolution of SC regions compared with experiments [53], as pointed out by Hong, et al. [59], it is still useful and convenient for predicting reasonable cavitation flow fields without requiring excessive resources. More detailed information of the “simplified flow field” CFD strategy, including solver setup, boundary conditions, mesh, and validation, can be found in the work by Sun, et al. [53] and Sun, et al. [39].

2.2. Computational case and evaluation criteria

The original model is the cone-shaped CGU with a diameter of 10 mm, a cylindrical height of 4.5 mm, and no incline angle; and the distance between the rotor and stator was set to 2 mm, which is consist with the geometry of the ARHCR utilized in our experiments [49]. To evaluate the effect of CGU arrangement on the ARHCR performance, 21 cases with various arrangements were conducted in this work, i.e., radial offset distance (c = 0, 0.5, 1, 1.5, and 2 mm), intersection angle (ω = 9°, 10°, 11.25°, 12°, and 15°), number of rows (N = 1, 2, 3, 4, and 5), circumferential offset angle (γ = 0°, 1°, 2°, 3°, and 4°), and radial spacing (r = 11, 12, 13, 14, and 15 mm). The corresponding specific structures are illustrated in Fig. 3 with the detailed information of structural factors in the sub-caption, and the detailed description can be found in the corresponding subsection in Section 3.

Fig. 3.

Schematic diagram of the models with various CGU arrangements.

HCRs can produce thermal energy and lead to a continuous rise in bulk temperature, affecting the chemical reaction rate and physical properties of reactants and the consequent bubble dynamics. Nevertheless, this study only focuses on the effect of the CGU arrangement on the performance, therefore, the effect of temperature is excluded in the “simplified flow field” numerical simulation.

In Pandur, et al. [60]’s work, they characterized the cavitation intensity by the peak hydrodynamic force and peak wall shear stress. These two factors can only be obtained in the simulation of bubble dynamics; and cannot be obtained in the simulation of macroscopic cavitating flow. In contrast, this work selected the total volume fraction of vapor, ${\alpha }_{\text{total}}$, which is a compromised and convenient parameter standing for the induced cavitation intensity, and is widely used in the simulation of macroscopic cavitating flow [39], [55].

$$V_{\text{vapor}}=\sum _{i=1}^N{\alpha }_{\text{vapor}}{V}_i$$ (1)

where $V_{\text{vapor}}$ is the cavitation volume, $N$ is the total number of cells in the computational domain, ${\alpha }_{\text{vapor}}$ is the vapor volume fraction of each cell, and $V_i$ is the volume of each cell. On the contrary, the energy consumption, i.e., the shaft power of the electric motor, can be partly represented by the total moment of the rotor, $\overrightarrow{M_{\text{z}}}$:

$$\overrightarrow{M_{\text{z}}}=\overrightarrow{r}\times \overrightarrow{F_{\text{p}}}+\overrightarrow{r}\times \overrightarrow{F_{\text{v}}}$$ (2)

where $\overrightarrow{r}$ is the vector from the moment center to the force origin, $\overrightarrow{F_{\text{p}}}$ is the pressure force vector, and $\overrightarrow{F_{\text{v}}}$ is the viscous force vector.

To intuitively show the performance of each model, the cavitation generation efficiency ($\eta$) representing the ratio of effectiveness to energy input was chosen as follows:

$$\eta =\frac{V_{\text{vapor}}}{\left|\overrightarrow{M_{\text{z}}}\right|}$$ (3)

The numbers of the total time step and iteration per time step were specified as 40 and 500, respectively, with a time step of 0.0625 ms. Because the strongest interaction effect between the static and moving CGUs appears just before the coinciding stage (i.e., 15.9375 ms) [53], the values of $V_{\text{avg}}$ and $\overrightarrow{M_{\text{z}}}$ were obtained at this moment for all cases in this study, to directly reveal the performance difference.

3. Results and discussions

To intuitively show the effect of various CGU arrangements on the cavitation performance, Fig. 4 shows the cavitation volume,$V_{\text{vapor}}$, and cavitation generation efficiency, η, for each case, and the detailed data can be found in Supplementary Table S1. To further analyze this, Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9 demonstrate the velocity and pressure distributions and cavitation pattern for each arrangement. Because the number of CGUs for the five arrangements is not identical, it should be noticed that evaluating the effect of different levels for one arrangement is preferable and the performance comparison among each arrangement may be meaningless, due to the limitation of the “simplified flow field” strategy. This will be discussed in Section 3.3 in detail.

Fig. 4.

Effect of various CGU arrangements on the performance ($V_{\text{vapor}}$: cavitation volume, $\eta$: cavitation generation efficiency, c: radial offset distance, ω: intersection angle, N: number of rows, γ: circumferential offset angle, and r: radial spacing).

Fig. 5.

Effect of radial offset distance, c, on the velocity and pressure distributions and cavitation pattern (ω = 11.25°, N = 1, γ = N/A, r = N/A). Upper: velocity distribution and streamline in absolute reference frame of the middle plane. Bottom: pressure distribution of the middle plane and rotor. The transparent white iso-surface is the cavitation with a gas volume fraction at 0.1.

Fig. 6.

Effect of intersection angle, ω, on the velocity and pressure distributions and cavitation pattern, corresponding to Fig. 5 (s = 0, N = 1, γ = N/A, r = N/A).

Fig. 7.

Effect of numbers of rows, N, on the velocity and pressure distributions and cavitation pattern (s = 0 mm, ω = 11.25°, γ = 0°, r = 13 mm), corresponding to Fig. 5.

Fig. 8.

Effect of circumferential offset angle, γ, on the velocity and pressure distributions and cavitation pattern (s = 0 mm, ω = 11.25°, N = 3, r = 13 mm), corresponding to Fig. 5.

Fig. 9.

Effect of radial spacing, r, on the velocity and pressure distributions and cavitation pattern (s = 0 mm, ω = 11.25°, N = 3, γ = 2°), corresponding to Fig. 5.

3.1. Effect of radial offset distance

The radial offset distance, c, between a pair of moving and static CGUs affects their interaction intensity and consequent cavitation generation. The magnitude of SC and VC regions changed dramatically as the c rose from 0 to 2 mm (Fig. 5 Bottom). Specifically, the $V_{\text{vapor}}$ and η were increased by 84.24% (from 4.353 to 8.020 × 10^-8 m³) and 87.88% (from 2.285 to 4.293 × 10^-8 m²/N) when the c was increased from 0 to 1 mm, respectively, as shown Fig. 4 (a); and further increasing c can attenuate this effect. Hence, a moderate c is recommended when designing an interaction-type ARHCR.

The effect of the c on the flow field is considerably complex, as it affects both the main flow and radial flow induced by the radial misalignment. For interaction-type ARHCRs, cavitation is normally induced by both the flow separation (i.e., the SC region) and the vortex inside the CGUs (i.e., the VC region) [53]. As the c gradually increased, the velocity gradient inside the CGUs became more obvious, as a result of the appropriate misalignment of the two CGUs (Fig. 5 Upper), leading to the formation of a greater low-pressure vortex region (Fig. 5 Middle). This region, caused by Kelvin-Helmholtz instability, can promote the growth of the VC regions, as shown in Fig. 5 (a)–(c) Bottom. When the c was further increased (e.g., 1.5 and 2 mm), the excessive misalignment suppressed the development space of the vortex and weakened the reverse flow after the flow impacted the downstream edge of the CGU wall, reducing the dimension of the formed VC regions (Fig. 5 (d)–(e) Bottom). It can be imagined that the two CGUs will not interact with each other for a sufficient c (e.g., when c is greater than the CGU radius). In the latter case, the interaction-type ARHCR will become a shear-type one.

Increasing the c can enlarge both the thickness and length of the SC regions. The aforementioned misalignment accelerated the impact flow (Fig. 5 Upper) and formed greater SC regions (Fig. 5 Bottom). Moreover, axial flows can be observed inside the two vortexes (Fig. 5 Upper). Increasing the c continuously enhanced the axial flow and caused a more violent impact on the CGU edge. As a result, this expanded upstream the low-pressure region existing on the downstream side of CGUs, forming a “local cavitation” region, which merged with the SC regions in the mainstream area (Fig. 5 (b)–(e) Bottom). It can be concluded that a proper radial misalignment between a pair of CGUs assuredly enhances the interaction intensity and the subsequent performance. In fact, these can be visually identified by the magnitude and size of the high-pressure region on the CGU wall. For instance, the most notable high-pressure region can be found in the cases of c = 1 and 1.5 mm (Fig. 5 (c)–(d)), which performed the highest η (4.293 and 4.201 × 10^-8 m²/N, respectively).

In the ARHCR, a large number of vortexes are formed due to the violent incoming flows. In general, by employing the second invariant of the velocity gradient tensor, the classical Q-criterion can successfully visualize the vortex structure in 3D cavitation flows generated by hydrofoils, propeller, etc. Vorticity, the curl of velocity fields, can partly represent the structural dimension of a vortex in 2D. Nevertheless, in this case, because of the narrow clearance flow field, high velocity gradient, and effect of boundary layer, vortexes became considerably complex and are hard to capture by utilizing both the above two quantities.

3.2. Effect of intersection angle

As the intersection angle, ω, rose, the VC region in the static CGU gradually shrank, and at the same time, the SC region on the downstream side of both the CGUs elongated, as shown in Fig. 6. The ω of 9°, 10°, 11.25°, 12°, and 15° corresponds to the ARHCR with 40, 36, 32, 30, and 24 CGUs in one row on the rotor and stator, respectively. It shoud be mentioned that due to the difference in ω in the five cases, the relative position of the static and moving CGUs in each case was not precisely identical, which may lead to minor errors.

The influence rule of the ω on the flow field is relatively simple. As for the development of VC region, smaller ω, corresponding to a greater number of CGU in a row, can enhance the intensity and frequency of interaction under the same operating condition, leading to larger VC regions as greater velocity gradient (Fig. 6 (a)–(c) Bottom). At the same time, the development of SC regions was restricted because a greater high-pressure region was generated in the clearance flow field due to the lower interaction frequency. This means that the interaction motion prematurely destroyed the SC region before its well-development. On the contrary, larger ω caused a longer interval of interaction period and the formation of the temporary non-interaction stage of CGUs, which both are unfavorable to the development of VC (Fig. 6 (d)–(e) Bottom). This may mainly cause a decrease in $V_{\mathit{vapor}}$ when ω changed from 11.25° to 12° (Fig. 4 (b)). The VC region in the static CGU even disappeared at a ω of 15°. While longer interaction frequency offered more room for the development of SC. The SC can almost reach the edge of the wall of the next CGU. The change in the interaction effect can be intuitively observed from the magnitude and area of the high-pressure regions on the CGU wall (Fig. 6 Bottom).

By quantitively evaluating the effect of ω according to Supplementary Table S1, increasing or decreasing the ω from the initial value seems to be profitable for the performance, and the η obtained the highest value (3.996 × 10^-8 m²/N) at ω = 12° which is 1.75 times that of the orginal model. However, it should be noticed that the presented data were obtained at only one moment, instead of the whole interaction cycle. Thus, a lower ω with a higher interaction frequency can clearly gain greater treatment effectiveness in unit time. Therefore, an appropriately lower c is more appropriate for the design of ARHCRs, even with more energy consumption.

3.3. Effect of number of rows

For interaction- or shear-type ARHCRs, adding more rows of CGUs on the rotor and/or stator can normally improve the treatment effectiveness, with a higher requirement of shaft torques, e.g., the reactors utilized in the works of Maršálek, et al. [61] and Chipurici, et al. [22]. At the same time, the relation between the enhanced performance and the number of rows does not exhibit a positive correlation (Fig. 4 (c) and Supplementary Table S1). This is because of various radial positions of rows, which affects the linear velocity and cavitation intensity of CGUs, and the mutual interference of CGUs in each row. Thus, it is important to evaluate the effect of numbers of rows, N, on the performance.

When the N became two, the low-pressure regions on the downstream side of the four CGUs were merged into a considerably wider low-pressure region, due to the flow disturbance between the CGUs in each row. This significantly extended and thickened all SC regions. Meanwhile, the flow disturbance also compressed the vortexes located in the two static CGUs (Fig. 7 (b) Upper), resulting in higher vortex velocities and larger VC regions (Fig. 7 (b) Bottom). While the VC region inside the outer moving CGU obviously contracted as the reduced vortex velocity. As a result, the $V_{\text{vapor}}$ and η were increased by 118.8% (from 4.353 to 9.525 × 10^-8 m³) and 12.7% (from 2.285 to 2.576 × 10^-8 m²/N), respectively, compared with the original model (Fig. 4 (c) and Supplementary Table S1). Interestingly, the $V_{\text{vapor}}$ of the former is greater than two times that of the latter, i.e., 9.525 × 10^-8 m³ > 8.706 × 10^-8 m³, signifying that an effective interaction between the CGUs in each row exactly existed.

On the contrary, further increasing the number of rows to 3–5 did not show a promising rise in the cavitation intensity but a rapid drop of η, as shown in Fig. 3 (c), e.g., 0.514 × 10^-8 m²/N for N = 5, which is only 1/5 that in the case of N = 2. Unlike the multiple growth of $\overrightarrow{M_{\text{z}}}$ with increasing N, for example, $\overrightarrow{M_{\text{z}}}$ for N = 5 is approximately five times that $\overrightarrow{M_{\text{z}}}$ for N = 2, the change in the $V_{\text{vapor}}$ and $\eta$ is not monotone increasing (Supplementary Table S1). This is mainly because with increasing N the fluids were easier to concentrate on the outer side, forming high-pressure regions due to the centrifugal effect. As a result, the VC and SC regions generated by outer CGUs significantly reduced or even vanished. Although the “simplified flow field” strategy utilized in this research could aggravate this issue because the flow field had no outlet (the radial flow “heaped” against the wall, this might be called as “sidewall effect”), the related results are still instructive for the design of ARHCRs. For both interaction- and shear-type ARHCRs, it is important to maintain a sufficient clearance between the side surfaces of the rotor and stator to ensure an adequate passing flow rate. In addition, an appropriate positive pressure difference between the inlet and outlet is also required.

Since the CGU number for the five cases was different and the time step in all simulations was identical, it cannot be guaranteed that the relative position of CGUs in all cases was perfectly identical. Nevertheless, the difference in the relative position of all cases was negligible and the above results were reasonable.

3.4. Effect of circumferential offset angle

The effect of circumferential offset angle, γ, has been ignored in the past, even though it is comparatively limited compared with the aforementioned factors (Fig. 4 (d)). The highest $V_{\text{vapor}}$ and η values appeared at γ = 2°.

According to Fig. 8, it can be confirmed that varying γ caused changes in the direction of the wake flow and consequent cavitation region, which was mentioned in Section 3.2. For γ = 1°, the interaction intensity was evidently improved, compared with that in the case of γ = 0°: The slight circumferential offset between the two pairs of the CGUs led to the wake flows, generated from the middle CGU and outside/inside CGU, merged with each other, resulting in subsequent accelerated incoming flow and enhanced interaction intensity (Fig. 8 (b)). This can be also confirmed by the unparallel streamlines in the clearance flow field and the enlarged high-pressure region on the CGU wall. As a consequence, greater SC and VC regions were induced, especially for the middle CGUs: The VC region inside the static CGU reappeared because of the highly twisted and accelerated vortex flow ((Fig. 8 (b) Upper).

Moreover, a new “small VC” region can be recognized inside the middle static CGU, and this implies that radial vortex flows, caused by the interaction of the wake flows, existed and their intensity was high enough to generate a VC region (Fig. 8 (b) Bottom). The size of this VC region can reflect the interaction intensity of the wake flow to a certain extent. In fact, the “small VC” region can be also observed in Fig. 5 (a)–(b) Bottom, Fig. 6 (b)–(c) Bottom, and Fig. 7 (a)–(b) Bottom, and may be considered as the origin of the VC region in the static CGU.

The aforementioned enhancement effect became more prominent in the case of γ = 2°, and the the $V_{\text{vapor}}$ and η were increased from 5.796 to 8.027 × 10^-8 m³ and 0.972 to 1.391 × 10^-8 m²/N, respectively, compared with the original model. Except for the SC and VC, it can be also found that the small VC region visibly grew. While as the γ further rose to 3° and 4°, the interaction effect of the wake flow was weakened, which can be confirmed by the parallel streamline in the clearance flow field (Fig. 8 (d)–(e) Left). This resulted in smaller cavitation regions and the consequent lower $V_{\text{vapor}}$ and η (Fig. 4 (d) and Supplementary Table S1).

In conclusion, the change in the γ affects the flow field and induces or inhibits the occurrence of cavitation region. A properly small γ is advisable for the accelerated incoming flow and enhanced interaction intensity.

3.5. Effect of radial spacing

After evaluating the influence of N and γ in 3.3, 3.4, respectively, it is worth further studying the effect of various radial spacings, r, on the performance. By analyzing the data in Fig. 4 (e) and Supplementary Table S1, it is found that the CGU with a relatively high or low r value resulted in a lower generation amount of cavitation. The development of SC progressively declined with an increase in r, and the development of VC initially increased and then decreased with increasing r (Fig. 9 Bottom).

The CGU with an r at 13 mm showed the highest performance. For the case with a small r (e.g., 11 or 12 mm), the interaction of the wake flows can be clearly recognized by the convergence of streamlines on the downstream side of CGUs, as presented in Fig. 9 (a), (b) Upper. Even though this led to the well development of the SC regions, the excessively strong interaction of the wake flows negatively influenced the formation of the vortexes and consequently, the development of VC regions. The reduced interaction intensity between one pair of CGUs can be affirmed by the decreased area of the high-pressure region on the CGU wall. When the radial spacing was further enlarged (14 or 15 mm), both the SC and VC regions became considerably smaller, because the two interaction effects were significantly weakened. In addition, the cavitation generated by the outer CGUs was also suppressed due to the short distance to the wall, i.e., the “sidewall effect” mentioned in Section 3.3.

4. Conclusions

The present work evaluated the effects of various CGU arrangements (i.e., radial offset distance (c), intersection angle (ω), number of rows (N), circumferential offset angle (γ), and radial spacing (r)) on the performance of an ARHCR by utilizing the “simplified flow field” CFD strategy. The corresponding findings are as follows.

• •CGUs with a proper c can largely improve the cavitation performance, for instance, the efficiency can be increased by 87.88% when increasing c from 0 to 1 mm.
• •A lower ω (i.e., a higher number of CGU) enhanced the intensity and frequency of interaction between the moving and static CGUs and the consequent performance.
• •A moderate N is desirable. Excessive rows of CGU significantly suppressed the cavitation development in the outer CGUs due to the “sidewall effect”.
• •CGUs with moderate γ and r can improve the performance because the change in them caused interaction of the wake flows among each row of CGUs, generating greater cavitation regions.

The present work also exposed the weakness of the “simplified flow field” strategy. For the cases with multirow CGUs, without outlets, the radial flow “heaped” against the sidewall of the stator due to high-speed rotation, and this caused false high-pressure region on the outer flow field and may excessively restrict the cavitation development in the outer region (i.e., the “sidewall effect”). In addition, it is hard to specify inlet and outlet boundary conditions on the flow field since it may be impossible to measure the corresponding data in the experiments. Therefore, the “simplified flow field” strategy is more adapted to simulate the case with a small number of rows. Nonetheless, the “sidewall effect” may be induced by the short distance between the outer CGU and the wall in this research.

It should be also mentioned that the obtained results were only qualitative evaluations of the effects of the arrangement of CGU based on CFD, which may offer reference value for future research in the design of ARHCRs, further experimental validations are required. In addition, this work only included the effect of single factor, and these factors demonstrated strong interaction effect, which requires a multi-objective optimization in the future.

CRediT authorship contribution statement

Xun Sun: Writing – original draft, Writing – review & editing, Funding acquisition, Conceptualization, Supervision. Gaoju Xia: Investigation, Writing – original draft. Weibin You: Resources. Xiaoqi Jia: Writing – review & editing. Sivakumar Manickam: Writing – review & editing. Yang Tao: Writing – review & editing. Shan Zhao: Writing – review & editing. Joon Yong Yoon: Writing – review & editing. Xiaoxu Xuan: Conceptualization.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following are the Supplementary data to this article: