Acoustic Radiation Research Articles

Enhancing acoustic levitation capacity through array geometry optimization

The contactless micromanipulation capability and microgravity environment provided by the acoustic levitation technology have excellent application prospects in many fields, such as droplet dynamics, solidification state physics, life sciences, etc. However, the applications are severely constrained by the limitation of the transducer power. In this paper, we explore an array geometry optimization framework to improve the levitation capability. First, the acoustic pressure attenuation and directional characteristics of commercial transducers are analyzed to uncover the mechanism of the array geometry affecting the acoustic radiation force (ARF). Second, based on the Gor'kov potential theory, the array geometry form of N-elements is derived, and the arrangement in the spherical ring (ASR) method is proposed to obtain the element coordinates. Then, spherical radius and array height are adjusted to obtain the optimal array geometry. On this basis, the directional angle of each transducer is further optimized. Finally, simulation and physical verification are carried out. The simulation results indicate that the ARF increases and then decreases with the spherical radius and array height, which are the existing maximum values. Directional angle optimization (DAO) can improve the ARF, particularly when the array height exceeds the sphere diameter. These findings are consistent with the analytical results. Notably, we built a prototype physical system, and the physical experiments showed that the optimized array improved the axial ARF by 201.2% and the radial ARF by 115.9% over the conventional array. The works presented in this paper offer a valuable design approach for acoustic levitation arrays, thereby contributing to the advancement and application of ultrasonic array levitation technology.

A Review of Ultrasonic Treatment in Mineral Flotation: Mechanism and Recent Development.

Ultrasonic treatment has been widely used in the mineral flotation process due to its advantages in terms of operational simplicity, no secondary pollutant formation, and safety. Currently, many studies have reported the effect of ultrasonic treatment on mineral flotation and shown excellent flotation performance. In this review, the ultrasonic mechanisms are classified into three types: the transient cavitation effect, stable cavitation effect, and acoustic radiation force effect. The effect of the main ultrasonic parameters, including ultrasonic power and ultrasonic frequency, on mineral flotation are discussed. This review highlights the uses of the application of ultrasonic treatment in minerals (such as the cleaning effect, ultrasonic corrosion, and desulfuration), flotation agents (such as dispersion and emulsification and change in properties and microstructure of pharmaceutical solution), and slurry (such formation of microbubbles and coalescence). Additionally, this review discusses the challenges and prospects of using ultrasonic approaches for mineral flotation. The findings demonstrate that the application of the ultrasonic effect yields diverse impacts on flotation, thereby enabling the regulation of flotation behavior through various treatment methods to enhance flotation indices and achieve the desired objectives.

Ultrasound Elastography in Benign Gynecology: A Scoping Review.

To perform a scoping review of the literature in which ultrasound elastography (UE) has been used in benign gynecology and identify avenues for its use in future research and clinical implementations. A structured search of EMBASE, Medline and Cochrane databases was conducted (last search date April 15th, 2022). Eligible studies included adult participants with female pelvic anatomy. English language papers focusing on the utility of ultrasound elastography applied to benign gynecology were included. Narrative reviews, conference abstracts, and letters to the editor were excluded. Two independent reviewers screened titles and abstracts for inclusion, a third reviewer was consulted in cases of disagreement. Study quality was assessed by a checklist for study implementation and elastography technique. Extracted data included elastography technology, gynecologic application, opportunities for clinical implementation, and strengths and limitations. The search returned 2026 studies. A total of 40 studies, published between 2013 and 2022, were retained for data extraction. Studies most frequently used shear wave elastography as the method of UE (n = 23), followed by strain elastography (n = 13) and acoustic radiation force impulse (n = 4). Most common clinical applications for UE were the diagnosis of adenomyosis and uterine fibroids (27.5%), assessment of pelvic floor muscle function (22.5%), and describing the elastic properties of polycystic ovaries (17.5%) and the uterine cervix (15.0%). Limitations of the technology were identified as the lack of published reference values for gynecologic organs and difficulties in assessing tissues deep to the transducer. Future research is needed to validate the use of ultrasound elastography in gynecology under both normal and pathologic conditions.

Compound Acoustic Radiation Force Impulse Imaging of Bovine Eye by Using Phase-Inverted Ultrasound Transducer.

In general, it is difficult to visualize internal ocular structure and detect a lesion such as a cataract or glaucoma using the current ultrasound brightness-mode (B-mode) imaging. This is because the internal structure of the eye is rich in moisture, resulting in a lack of contrast between tissues in the B-mode image, and the penetration depth is low due to the attenuation of the ultrasound wave. In this study, the entire internal ocular structure of a bovine eye was visualized in an ex vivo environment using the compound acoustic radiation force impulse (CARFI) imaging scheme based on the phase-inverted ultrasound transducer (PIUT). In the proposed method, the aperture of the PIUT is divided into four sections, and the PIUT is driven by the out-of-phase input signal capable of generating split-focusing at the same time. Subsequently, the compound imaging technique was employed to increase signal-to-noise ratio (SNR) and to reduce displacement error. The experimental results demonstrated that the proposed technique could provide an acoustic radiation force impulse (ARFI) image of the bovine eye with a broader depth-of-field (DOF) and about 80% increased SNR compared to the conventional ARFI image obtained using the in-phase input signal. Therefore, the proposed technique can be one of the useful techniques capable of providing the image of the entire ocular structure to diagnose various eye diseases.

Magnetic resonance elastography (MRE) outperforms acoustic force radiation impulse (ARFI) in predicting oesophageal varices in obese NAFLD cirrhosis.

Liver stiffness measurement (LSM) by transient elastography has been shown to underperform in high-risk varices (HRVs) prediction in obese non-alcoholic fatty liver disease (NAFLD) compensated cirrhosis (CC). LSM by magnetic resonance elastography (MRE) and acoustic force radiation impulse (ARFI) has been shown to be useful in prediction of oesophageal varices (EVs), but has limited evidence in obese NAFLD-CC. Obese patients with NAFLD-CC who underwent MRE and ARFI for LSM and endoscopy for screening of varices were enrolled. Performance of MRE and ARFI for predicting EVs or HRVs was evaluated using area under receiver operating characteristics (AUROC) curves and regression analyses were performed for predictor variables. One hundred eight patients [mean age 54.7 ± 9.6years, median BMI, 28.5 (26.4-30.0) kg/m2. 72.2% diabetics, 45.4% hypertensive] were enrolled. Fifty-two (48.1%) had no varices, while 29 (26.8%) and 27 (25%) had low-risk varices (LRVs) and HRVs, respectively. MRE-LSM was higher in patients with LRVs (p = 0.01) or HRVs (p = 0.001) against those without varices. ARFI-LSM did not differ significantly between those without and with LRVs or HRVs (p > 0.05 for all). There was a low correlation between ARFI-LSM and MRE-LSM in the overall cohort (r = 0.19). Only platelet count (PC) [0.98 (0.97-0.99)] and MRE-LSM [1.8 (1.26-2.79)] were predictors of HRVs. At a cut-off of 4.75, MRE showed a sensitivity of 96.3%. Model combining MRE-LSM with PC had a diagnostic AUROC of 0.77 and 0.76 for EVs and HRVs. In obese NAFLD-CC, MRE-LSM is significantly higher in patients with varices. MRE combined with PC predicts EVs and HRVs with better accuracy than ARFI.

Density-contrast induced inertial forces on particles in oscillatory flows

Oscillatory flows have become an indispensable tool in microfluidics, inducing inertial effects for displacing and manipulating fluid-borne objects in a reliable, controllable and label-free fashion. However, the quantitative description of such effects has been confined to limit cases and specialized scenarios. Here we develop an analytical formalism yielding the equation of motion of density-mismatched spherical particles in oscillatory background flows, generalizing previous work. Inertial force terms are systematically derived from the geometry of the flow field together with analytically known Stokes number dependences. Supported by independent, first-principles direct numerical simulations, we find that these forces are important even for nearly density-matched objects such as cells or bacteria, enabling their fast displacement and separation. Our formalism thus consistently incorporates particle inertia into the Maxey–Riley equation, and in doing so provides a generalization of Auton's modification to added mass, as well as recovering the description of acoustic radiation forces on particles as a limiting case.

Programmable spin and transport of a living shrimp egg through photoacoustic pressure.

In the fields of biomedicine and microfluidics, the non-contact capture, manipulation, and spin of micro-particles hold great importance. In this study, we propose a programmable non-contact manipulation technique that utilizes photoacoustic effect to spin and transport living shrimp eggs. By directing a modulated pulsed laser toward a liquid-covered stainless-steel membrane, we can excite patterned Lamb waves within the membrane. These Lamb waves occur at the interface between the membrane and the liquid, enabling the manipulation of nearby particles. Experimental results demonstrate the successful capture, spin, and transport of shrimp eggs in diameter of 220 µm over a distance of about 5 mm. Calculations indicate that the acoustic radiation force and torque generated by our photoacoustic manipulation system are more than 299.5 nN and 41.0 nN·mm, respectively. The system surpasses traditional optical tweezers in terms of force and traditional acoustic tweezers in terms of flexibility. Consequently, this non-contact manipulation system significantly expands the possibilities for applications in various fields, including embryo screening, cell manipulation, and microfluidics.

Unveiling Acoustic Cavitation Characterization in Opaque Chambers through a Low-Cost Piezoelectric Sensor Approach

This study investigates the characterization of acoustic cavitation in a water-filled, opaque chamber induced by ultrasonic waves at 20 kHz. It examines the effect of different acoustic radiator geometries on cavitation generation across varying electrical power levels. A cost-effective piezoelectric sensor, precisely positioned, quantifies cavitation under assorted power settings. Two acoustic radiator shape configurations, one with holes and another solid, were examined. The piezoelectric sensor demonstrated efficacy, corroborating with existing literature, in measuring acoustic cavitation. This was achieved through the Fast Fourier Transform (FFT) analysis of voltage data, specifically targeting sub-harmonic patterns, thereby providing a robust method for cavitation detection. Results demonstrate that perforated geometries enhance cavitation intensity at lower power levels, while solid shapes predominantly affect cavitation axially, exhibiting decreased activity at minimal power. The findings recommend using two different shape geometries on the acoustic radiator for efficient cavitation detection, highlighting intense cavitation on radial walls and cavitation generation on the bottom. Due to the stochastic nature of cavitation, averaging data is critical. The spatial limitation of the sensor necessitates prioritizing specific areas over complete coverage, with multiple sensors recommended for comprehensive cavitation pattern analysis.

Comparison of Acoustic Radiation Characteristics in the Near and Far Fields Due to the Vibration of a Circular Disk Placed on an Infinite Rigid Baffle Using the Rayleigh Integral Method and Lumped Parameter Method

Comparison of Acoustic Radiation Characteristics in the Near and Far Fields Due to the Vibration of a Circular Disk Placed on an Infinite Rigid Baffle Using the Rayleigh Integral Method and Lumped Parameter Method

On the application of acoustic liners for the reduction of jet-flap installation noise

In this work, an experimental and numerical analysis of the feasibility of using acoustic liners to reduce the acoustic far-field radiation of a subsonic jet near a flat plate is presented. The Boundary Element Method (BEM) with a wavepacket model of the jet noise and considering an acoustic impedance boundary condition was used to calculate the far-field noise for different conditions. A parametric optimization was performed in order to find an optimum impedance in terms of the Overall Sound Pressure Level reduction. Semi-empirical models of acoustic liners were then used to design a liner with an impedance as close as possible to the optimum impedance. The liners were built using additive manufacturing and tested in terms of their acoustic impedance and the resulting noise reduction when applied to a region of the flat plate. The BEM simulations, considering the impedance, showed good agreement with experimental data. Overall, by means of the BEM model, optimization and liner semi-empirical models, it was possible to design an acoustic liner which significantly reduced the installation noise at the far-field, with the overall noise reduction between 2 dB to 4 dB depending on observation angle.

The Efficiency of Acoustic Radiation Force Impulse (ARFI) Elastography in the Differentiation of Renal Cell Carcinoma and Oncocytoma.

This study is to investigate the effectiveness of Acoustic Radiation Force Impulse (ARFI) elastography in differentiating radiologically similar renal cell carcinoma (RCC) and oncocytoma in solid masses of the kidney. The patients with solid renal mass histopathological diagnosed after excision or tru-cat biopsy who underwent a preoperative ARFI elastography of the lesion during a 4-year period were included in this study. Preoperative shear wave velocity (SWV) values were measured in all the lesions. SWV results of RCCs and oncocytomas were compared by an independent t-test, and cut-off, sensitivity and specificity values were calculated. Forty-two of the 60 patients included in the study were men (70%) and, 18 were women (30%), and the mean age was 59.7 ± 14 (27-94) years. Among 46 RCCs (76.6%), 23 and 14 oncocytomas, 5 (23.4%) were located in the right kidney (p:0.34722). Mean SWV values were found to be significantly higher in RCCs (2.87± 0.74 (0.96-4.14) m/s) than oncocytomas (1.83 ± 0.78 (0.80-3.76) m/s) (p <0.001). In the ROC analysis, a cutoff value of 2.29 m/s was found to havean 80.4% sensitivity and a 78.6% specificity for the discrimination of RCCs from oncocytomas. ARFI elastography measurements may be useful in distinguishing RCC and oncocytomas that may have similar solid radiological imaging features.

Customized and high-performing acoustic levitators for contact-free experiments

Acoustic levitators are becoming increasingly common research instrumentation for contact-free, lab-in-a-droplet studies. Recently, levitators that employ multiple, small, ultrasonic transducers have gained popularity, given their low price, temperature and spatial stability, low voltage, and accessibility. Yet, the current state-of-the-art device, TinyLev, presents limitations for certain applications in terms of stability, strength, and compactness. Herein, we developed three new levitators and evaluated the effect of the construction parameters (e.g., distance of opposing arrays, number and arrangement of transducers, etc.) on their performance. The best performing levitator from this work had half the number of transducers, compared to TinyLev, though presented 1.7 and 3.5 times higher levitation capacity along the horizontal and vertical configurations, respectively, and 4.7 and 2.0 times higher horizontal and vertical stability of a levitated object, respectively. Additionally, we present a direct means to evaluate the acoustic radiation net force acting on a deformable object for uniaxial levitators, without the use of a microphone or a schlieren deflectometer for this type of levitators. The theoretical and experimental observations provide insights for adapting the acoustic levitator design for specific applications. Finally, we developed an open-source software which allows the evaluation of the acoustic pressure field generated by customized designs and provides the necessary files for 3D printing the scaffold of the levitator. This study aims to increase accessibility and promote further developments in contact-free experiments.

Metabolic-Glycoengineering-Enabled Molecularly Specific Acoustic Tweezing Cytometry for Targeted Mechanical Stimulation of Cell Surface Sialoglycans.

In this study, we developed a novel type of dibenzocyclooctyne (DBCO)-functionalized microbubbles (MBs) and validated their attachment to azide-labelled sialoglycans on human pluripotent stem cells (hPSCs) generated by metabolic glycoengineering (MGE). This enabled the application of mechanical forces to sialoglycans on hPSCs through molecularly specific acoustic tweezing cytometry (mATC), that is, displacing sialoglycan-anchored MBs using ultrasound (US). It was shown that subjected to the acoustic radiation forces of US pulses, sialoglycan-anchored MBs exhibited significantly larger displacements and faster, more complete recovery after each pulse than integrin-anchored MBs, indicating that sialoglycans are more stretchable and elastic than integrins on hPSCs in response to mechanical force. Furthermore, stimulating sialoglycans on hPSCs using mATC reduced stage-specific embryonic antigen-3 (SSEA-3) and GD3 expression but not OCT4 and SOX2 nuclear localization. Conversely, stimulating integrins decreased OCT4 nuclear localization but not SSEA-3 and GD3 expression, suggesting that mechanically stimulating sialoglycans and integrins initiated distinctive mechanoresponses during the early stages of hPSC differentiation. Taken together, these results demonstrated that MGE-enabled mATC uncovered not only different mechanical properties of sialoglycans on hPSCs and integrins but also their different mechanoregulatory impacts on hPSC differentiation, validating MGE-based mATC as a new, powerful tool for investigating the roles of glycans and other cell surface biomolecules in mechanotransduction.

Using Local Concentration to Model the Progress of Acoustophoretic Assembly of Microspheres in Planar Standing Waves

Abstract Acoustophoretic assembly uses a standing acoustic field to move dispersed small particles into a geometric pattern. The technique relies on the acoustic radiation force, which arises from the interaction between the acoustic field and the particles, and drives the particles towards areas of low acoustophoretic potential. Acoustophoretic assembly shows potential for a wide range of applications, including organizing filler materials in composites, creating metamaterials, and fabricating functional biological tissue. However, the method has not yet been incorporated into large-scale manufacturing processes. One barrier is the incomplete understanding of the assembly process. While an ideal final pattern geometry can be calculated from the acoustic field and the material properties, there are currently no widespread metrics for measuring the progress of the pattern formation. As a result, it is difficult to know how long the acoustic field should be applied during manufacturing. Our approach uses the local particle concentration to model the acoustophoretic assembly process. We show that an expression for the time-dependent local particle concentration can be derived from the force balance on the particles and a control volume analysis. The analysis is applied to microspheres in a planar acoustic standing wave, and an analytical expression is obtained, , which yields a time parameter for pattern assembly and suggests a cut-off time. We then use the local concentration to define measurements for the quality of the assembled microsphere pattern. Experiments were carried out using polystyrene microspheres in a glycerol-water mixture to validate the theoretical results.

Acoustic radiation from multilayered materials using the reciprocity principle.

Application of the reciprocity principle to evaluate the acoustic radiation from arbitrary multilayered fluid and solid materials is described. To include the effect of shear motion in surrounding media, including viscosity in a fluid, equations for the acoustic radiation from such materials under point force excitation are developed in terms of reflection and transmission coefficients for longitudinal and shear waves. Calculations for forcing on either side of the layered material and in arbitrary directions, and for any asymmetric layer arrangements, are conducted. The frequency range of the calculations is not restricted by thin-plate or thick-plate theory. The test case for the radiation from plates embedded in a viscous and attenuating fluid has been investigated in detail. The effect of viscosity and attenuation has been quantified and shown to be significant at high frequencies. Application to the problem of flow noise is also briefly discussed.

Multi‐Frequency Ultrasound Directed Self‐Assembly

AbstractUltrasound‐directed self‐assembly (DSA) utilizes the acoustic radiation force associated with a standing ultrasound wave field to organize particles dispersed in a fluid medium into specific patterns. State‐of‐the‐art ultrasound DSA methods use single‐frequency ultrasound wave fields, which only allow organizing particles into simple, periodic patterns, or require a large number of ultrasound transducers to assemble complex patterns. In contrast, this work introduces multi‐frequency ultrasound wave fields to organize particles into complex patterns. A method is theoretically derived to determine the operating parameters (frequency, amplitude, phase) of any arrangement of ultrasound transducers, required to assemble spherical particles dispersed in a fluid medium into specific patterns, and experimentally validated for a system with two frequencies. The results show that multi‐frequency compared to single‐frequency ultrasound DSA enables the assembly of complex patterns of particles with substantially fewer ultrasound transducers. Additionally, the method does not incur a penalty in terms of accuracy, and it does not require custom hardware for each different pattern, thus offering reconfigurability, which contrasts, e.g., acoustic holography. Multi‐frequency ultrasound DSA can spur progress in a myriad of engineering applications, including the manufacturing of multi‐functional polymer matrix composite materials that derive their structural, electric, acoustic, or thermal properties from the spatial organization of particles in the matrix.

Three-Dimensional Shear Wave Elastography Using Acoustic Radiation Force and a 2-D Row-Column Addressing (RCA) Array.

Acoustic radiation force (ARF)-based shear wave elastography (SWE) is a clinically available ultrasound imaging mode that noninvasively and quantitatively measures tissue stiffness. Current implementations of ARF-SWE are largely limited to 2-D imaging, which does not provide a robust estimation of heterogeneous tissue mechanical properties. Existing 3-D ARF-SWE solutions that are clinically available are based on wobbler probes, which cannot provide true 3-D shear wave motion detection. Although 3-D ARF-SWE based on 2-D matrix arrays have been previously demonstrated, they do not provide a practical solution because of the need for a high channel-count ultrasound system (e.g., 1024-channel) to provide adequate volume rates and the delicate circuitries (e.g., multiplexers) that are vulnerable to the long-duration "push" pulses. To address these issues, here we propose a new 3-D ARF-SWE method based on the 2-D row-column addressing (RCA) array which has a much lower element count (e.g., 256), provides an ultrafast imaging volume rate (e.g., 2000 Hz), and can withstand the push pulses. In this study, we combined the comb-push shear elastography (CUSE) technique with 2-D RCA for enhanced SWE imaging field-of-view (FOV). In vitro phantom studies demonstrated that the proposed method had robust 3-D SWE performance in both homogenous and inclusion phantoms. An in vivo study on a breast cancer patient showed that the proposed method could reconstruct 3-D elasticity maps of the breast lesion, which was validated using a commercial ultrasound scanner. These results demonstrate strong potential for the proposed method to provide a viable and practical solution for clinical 3-D ARF-SWE.

Bridge-Borne Noise Induced by High-Speed Freight Electric Multiple Units: Characteristics, Mechanisms and Control Measures

The high-speed freight electric multiple unit (EMU) is one of the important development directions for railway freight transportation. To investigate the bridge radiation noise induced by the freight EMU, a noise prediction model consisting of the containers–vehicle–track–bridge dynamic model, finite element model, and boundary element model are established and validated. Through simulation, the bridge radiation noise under different train loading conditions is compared, and the noise radiation mechanism is revealed. Moreover, the noise reduction effect of the noise wall is studied, and the influences of noise wall heights and sound absorption materials are investigated. Results indicate that the bridge sound power and the sound pressure levels (SPLs) of near-field points increase slightly with train loads in the frequency range below 20 Hz and above 125 Hz, with a maximum increase of about 6.8 dB. The structure resonance, intense local vibration, and high acoustic radiation efficiency cause strong bridge radiation noise. The noise wall can realize a good overall noise reduction effect in the sound shadow zone; nevertheless, SPLs increased in areas between the bridge and the noise wall. The ground reflection affects the superposition of transmitted, reflected, and diffracted sound waves, which causes nonlinear relationships of noise reduction effects with the noise wall height. From the perspective of human hearing sensitivity, the loudness levels of typical field points increase with the frequency in the range of 20~80 Hz, and SPLs below 25 Hz are less than the threshold of hearing. Setting the noise wall can effectively reduce the loudness levels, and the reduction effect increases with the noise wall height.

Transdermal drug delivery mediated by acoustic vortex beam

Ultrasound-mediated transdermal drug delivery exhibits various advantages such as biocompatibility, controllability and safety, which attracts plenty of interests within biomedical field. Current researches mostly emphasizes the acoustic cavitation generated by planar or focused waves while neglecting other physics that occur during transportation. Our experimental study illustrates the presence of an acoustic vortex (AV) beam that exhibits a lower acoustic intensity and typically means a lower dose of inertial cavitation, yet achieves a more efficient delivery. Such a result calls for the fundamental mechanism of ultrasound-mediated transdermal transfer using the AV beam. In this work, according to our knowledge, the AV beam is firstly introduced to ultrasound-mediated transdermal medication delivery. The transversal acoustic radiation force (T-ARF), which is the primary characteristic carried by the acoustic vortex beam, and its contribution to the transport enhancement are investigated. It is shown that a focused AV (FAV) beam with a maximal acoustic pressure of 200 kPa induces a pN-level T-ARF, which promotes the enlargement of pores on the stratum corneum and thereby enhances the permeability, as compared with a zero-order (non-vortex) counterpart. This contribution of the T-ARF is validated by the experimental transport on the cellulose membrane, which exhibits a significantly increased membrane porosity and delivery efficiency. The favorable results introduce the new degree of freedom into the ultrasound-mediated transdermal drug transport based on AV beam, and thereby promotes the development of a combined control strategy for more precise and efficient transdermal drug delivery in conjunction with the administration of acoustic cavitation.

Smart Blade Count Selection to Align Modal Propagation Angle with Stator Stagger Angle for Low-Noise Ducted Fan Designs

The rotor–stator interaction noise is a major source of fan noise. Especially for low-speed fan stages, the tonal component is typically a dominant noise source. A challenge is to reduce this tonal noise, as it is typically perceived as unpleasant. Therefore, in this paper, we analytically, numerically and experimentally investigate an acoustic effect to lower the tonal noise excitation. Our study on an existing low-speed fan indicates a reduction in tonal interaction noise of more than 9 dB at the source if the excited acoustic modes propagate parallel to the stator leading edge angle. Moreover, a design-to-low-noise approach is demonstrated in order to apply this effect to two new fan stages with fewer stator than rotor blades. The acoustic design of both fans is determined by an appropriate choice of the rotor and stator blade numbers in order to align the modal propagation angle with the stator stagger angle. The blade geometries are obtained from aerodynamic optimization. Both fans provide similar aerodynamic but opposing acoustic radiation characteristics compared to the baseline fan and a significant tonal noise reduction resulting from the impact of the modal propagation angle on noise excitation. To ensure that this effect can also be applied to other low-speed fans, a design rule is derived and validated.