Géza Pattantyús-Ábrahám Doctoral School of Mechanical Engineering 

BME Faculty of Mechanical Engineering, Department of Fluid Mechanics

Supervisor: Dr. VAD János

Preliminary study on noise and vibration generation of vortices shedding from turbomachinery blades

Introducing the research area

The global commercial market for unmanned aerial vehicles (UAVs) and micro aerial vehicles (MAVs) is projected to exhibit a compound annual growth rate (CAGR) of 26% until 2030. This trend poses a major challenge in terms of noise pollution, which is considered one of the leading health issues in Europe after air pollution, according to the European Environmental Agency. Consequently, the Turbomachinery research group at the Department of Fluid Mechanics is dedicated to studying drones, as well as small-diameter and/or low-speed fans, which are used, for instance, for cooling computer CPUs and electric motors. These turbomachieries often operate in close proximity to the user, making the reduction of noise and vibration crucial from an engineering perspective, ensuring the protection of human health, comfort, and reliable operation.

Brief introduction of the research place

My research is being conducted at the Department of Fluid Mechanics of the Faculty of Mechanical Engineering BUTE, under the supervision of Dr. János Vad, the current Head of the Department. Our department is one of the few research institutions in Hungary that focuses on fluid mechanics and has been awarded the title of Excellent Research Infrastructures in Hungary in 2021. Our laboratory, named after the renowned Hungarian aerodynamicist Theodore von Kármán, offers unique measurement opportunities in Central Europe due to its capacity and instrumentation. Besides educating future engineers, we also engage in research and development activities for industries where fluid mechanics, acoustics, turbomachinery, atmospheric flows, vehicle aerodynamics, and environmental engineering play a significant role.

History and context of the research

The studied turbomachinery shows a common feature of operating within a moderate range of chord-based Reynolds numbers, where Re ≤ 150,000 serves as a reference. In this moderate Reynolds number range, one of the possible main mechanisms for noise and vibration generation [1-3] is profile vortex shedding (PVS), which leads to the periodic shedding of coherent vortices from the blades. The phenomenon is alternatively referred to as laminar-boundary-layer vortex shedding [4].

 

Figure 1: Illustration for PVS [5] and its main characteristics.

The dominant frequency of vortex shedding plays a crucial role in assessing both aeroacoustic and mechanical effects. The literature [5,6] derives the universal Strouhal number (St*) characterizing vortex shedding as follows:

 

 

in accordance with Fig. 1: f represents the frequency of vortex shedding; b is the distance between the shedding vortex rows perpendicular to the blade chord; U denotes the free-stream velocity. The term "universal" originates from the fact that its value is considered [5,6] to be universally valid for various symmetrical blade profiles, Reynolds numbers, and angles of attack.

 

The above illustrates that from an engineering perspective, it is essential to determine both the dominant frequency (f) of vortex shedding and the distance between shedding vortices perpendicular to chord (b). Knowing these characteristics – and utilizing the constancy of St* – the frequency of vortex shedding can be estimated semi-empirically [7], even in the preliminary design phase.

The research goals, open questions

The literature on PVS discusses relatively thick, symmetrical blade profiles out of the NACA-00 series (Fig. 1). Such profiles are unusual for turbomachinery. Therefore, one of my research objectives is to extend the measurement-based literature on PVS to asymmetrical blade profiles (Fig. 2) that represent turbomachinery applications.

 

 

Figure 2: Asymmetrical blade profiles. Left: RAF-6E, right: 8% cambered plate.

 

To determine the distance b, the vortex centers within the pair of rows of shed vortices are to be localized. In the experiments in Refs. [5,6,8], the maxima of root-mean-square (RMS) of velocity fluctuation (see Fig. 3) – measured in the wake behind the blade profile – were considered as loci of the axes of shed vortices in vortex rows. In other words, the largest velocity fluctuations are attributed to the shedding vortices. Additionally, b approximately corresponds to half the width of the mean velocity distribution. It is important to note that the latter statement is not confirmed by the literature. Therefore, my research aims to elaborate and validate an analytical model for supporting the measurement-based determination of the distance b.

Methods

Measurement technique

Wind tunnel measurements were performed on models of asymmetrical blade profiles (Fig. 2) at various Reynolds numbers and angles of attack (α). The flow velocity in the near-wake region was measured using a single-component hot-wire. Fig. 3 shows illustrative examples of the measured velocity distributions.

Figure 3: Hot-wire measurement. Left: fluctuating velocity RMS, right: temporal mean velocity.

 

Computational Fluid Dynamics (CFD)

Besides measuring the velocity distributions, two-dimensional CFD simulations were carried out to better understand the resulting flow phenomena. It is achieved via the finite volume method, where the geometrical model of the flow domain is divided into small cells (meshing), and appropriate boundary conditions are specified on the interfaces. By solving the governing equations of fluid flow (mass and momentum conservation, effects of turbulence, etc.) on the numerical mesh, the characteristics of the flow can be determined (Fig. 4).

 

Figure 4: CFD results. Left: static pressure [Pa], right: velocity magnitude [m/s].

 

Vortex detection

The definition of a vortex remains debated in fluid mechanics; however, it has two widely accepted characteristics. Firstly, vortices are considered concentrated regions of high angular velocity. Secondly, they preserve the embedded fluid particles. Based on these characteristics, the authors of [9] have developed an objective vortex detection algorithm. Processing the velocity field data obtained, for example, through CFD simulations, the algorithm identifies the centers and boundaries of shedding vortices (Fig. 5).

 

Figure 5: Vortex detection based on [9] (TE: trailing edge).

Results

Extension of universal Strouhal number to asymmetrical airfoils

By evaluating the data acquired from the hot-wire measurements (where b is determined from the RMS distributions of velocity fluctuations and f is derived through fast Fourier transform), the universal Strouhal number can be computed for each measurement case:

 

Figure 6: Universal Strouhal number for asymmetrical blade profiles.

 

Based on Fig. 6, the range of the universal Strouhal number is St* = 0.19 ± 0.03, taking into account the uncertainties of the measurements. Therefore, considering this range, the applicability of the "universal" Strouhal number can be extended to asymmetrical blade profiles.

 

Analytical model: shear layer equation

With the use of the momentum and mass conservation equations, an analytical model for a simplified description of the flow field dominated by vortex shedding has been developed [S10]. According to the resulting shear layer equation, the shedding vortices are expected to pass through the inflection points (IP) of the mean velocity distribution (right side of Fig. 3). For illustration purposes, the motion of a representative suction-pressure side vortex pair compared to the IPs of the mean velocity distribution is shown in the right-side Fig. 7. To quantify this behavior, the rolling average of the deviation of the vortex centers from the IP was calculated.

Figure 7: Left: illustration for vortex trajectories, right: rolling average of deviations.

 

It can be observed that near the trailing edge, where one assumption of the analytical model is violated, the agreement not that satisfactory. However, further away, the average deviations converge to zero. Therefore, at a given X location in the wake, the expected value of the positions of the suction and pressure side vortex centers in the Y direction, perpendicular to the inflow (X), corresponds to IPs of the mean velocity distribution.

Expected impact and further research

By extending St* to asymmetrical blade profiles, the semi-empirical model in the literature can be further developed. The analytical model allows for predicting the dispersion of the blade wake and the broadening of the frequency range of vortex noise. These factors play a key role in the investigation of the interaction and noise of drone rotors. The prospective results of my research contribute to further enhanced design guidelines for moderating the noise and vibration of turbomachinery. Our publication [S7] received the "Best Paper Award" from the Fans and Blowers Committee at the prestigious ASME Turbo Expo conference in 2022, demonstrating the international embedding and recognition of our research. Findings have been shared at prominent international forums; there is active communication with foreign research groups paving the way for future collaborations.

 

 

Publications, references, links

List of corresponding own publications

[S1] G. Daku, J. Vad, "Experiment-Based Preliminary Design Guidelines for Consideration of Profile Vortex Shedding from Low-Speed Axial Fan Blades," in ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, Virtual Conference, Paper ID: GT2020-75778, 12 p., September 21–25, 2020.

[S2] G. Daku, J. Vad, "Mérés-alapú előtervezési irányelvek axiális ventilátor-lapátokról leúszó örvények figyelembe vételére," in XXVIII. Nemzetközi Gépészeti Konferencia – OGÉT 2020, Cluj, Romania, pp. 97–100., 2020.

[S3] G. Daku, J. Vad, "Experiment-Based Preliminary Design Guidelines for Consideration of Profile Vortex Shedding from Low-Speed Axial Fan Blades," Journal of Turbomachinery -Transactions of the ASME, vol. 143, no. 1, 10 p., 2021.

[S4] G. Daku, J. Vad, "Profile vortex shedding from low-speed axial fan rotor blades: a modeling overview," Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, vol. 236, no. 2, pp. 349-363, 2021.

[S5] G. Daku, J. Vad, "Semi-Empirical Design Guidelines for Controlling the Vibration and Noise of Low-Speed Axial Fans due to Profile Vortex Shedding, " in Proceedings of 14th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics (ETC’14), Gdansk, Poland, Paper: ETC2021-546, 14 p., April 12 – 16, 2021.

[S6] G. Daku and J. Vad, "Preliminary Design Guidelines for Considering the Vibration and Noise of Low-Speed Axial Fans Due to Profile Vortex Shedding," International Journal of Turbomachinery, Propulsion and Power, vol. 7, no. 1, 23 p., 2022.

[S7] G. Daku and J. Vad, "A Comprehensive Analytical Model for Vortex Shedding from Low-Speed Axial Fan Blades," in ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition, Rotterdam, The Netherlands, Paper ID: GT2022-80190, 13 p., June 13 – 17, 2022.

[S8] P. Ferenczy, E. Balla, T. Benedek, G. Daku, B. Kocsis, A. Kónya, J. Vad, “Development of a radial flow fan family for contaminated gases of relatively high flow rate,” Conference on Modelling Fluid Flow (CMFF’22), Budapest, Hungary, Paper ID: CMFF22-048, 12 p., August 30 - September 2, 2022.

[S9] B. Kocsis, T. Benedek, P. Ferenczy, E. Balla, G. Daku, J. Vad, ”Aerodynamic and acoustic studies on a radial fan family developed for increased specific flow rate of dust-laden gases,” in Proceedings of 15th European Conference on Turbomachinery Fluid Dynamics and Thermodynamics (ETC’15), Budapest, Hungary, Paper ID: ETC2023-126, 15 p., April 24 - 28, 2023.

[S10] G. Daku, J. Vad, "A Comprehensive Analytical Model for Vortex Shedding from Low-Speed Axial Fan Blades," Journal of Turbomachinery -Transactions of the ASME, vol. 145, no. 7, 11 p., 2023.

 

Table of links

Drone market size forecast

European Environmental Agency

Turbomachinery research group

Department of Fluid Mechanics

Faculty of Mechanical Engineering BUTE

Dr. János Vad

Excellent Research Infrastructures in Hungary in 2021

Theodore von Kármán wind tunnel laboratory

Reynolds number

Strouhal number

Hot-wire anemometry

Computational Fluid Dynamic (CFD)

Fast Fourier transform

ASME Turbo Expo

List of references

[1] C. Lee, M. K Chung, Y. H. Kim, "A prediction model for the vortex shedding noise from the wake of an airfoil or axial flow fan blades," Journal of Sound and Vibration, vol. 164(2), pp. 327–336, 1993.

[2] S. Sasaki, Y. Kodama, H. Hayashi, M. Hatakeyama, "Influence of the Karman vortex street on the broadband noise generated from a multiblade fan," Journal of Thermal Science, vol. 14(3), pp. 198–205, 2005.

[3] H. Dou, Z. Li, P. Lin, Y. Wei, Y. Chen, W. Cao, H. He, "An improved prediction model of vortex shedding noise from blades of fans," Journal of Thermal Science, vol. 25(6), pp. 526–531, 2016.

[4] T. F. Brooks, D. S. Pope, M. A. Marcolini, " Airfoil self-noise and prediction," NASA Reference Publication, NASA-RP-1219, 1989.

[5] S. Yarusevych, P. E. Sullivan, J. G. Kawall, "On vortex shedding from an airfoil in low- Reynolds-number flows, Journal of Fluid Mechanics," vol. 632, pp. 245–271, 2009.

[6] S. Yarusevych, M. S. H. Boutilier, "Vortex shedding of an airfoil at low Reynolds numbers," AIAA Journal, vol. 49, pp. 2221–227, 2011.

[7] E. Balla, J. Vad, “Refinement of a Semi-Empirical Method for the Estimation of Profile Vortex Shedding Frequency from Low-Speed Axial Fan Blade Sections,” Proceedings of the 14th European Conference on Turbomachinery Fluid Dynamics & Thermodynamics, ETC14, Gdansk, Poland (Online), Apr. 12–16, 2021, Paper No. ETC2021-591.

[8] A. Roshko, “On the Development of Turbulent Wakes from Vortex Streets,” NACA Report 1191, 1954. https://ntrs.nasa.gov/citations/19930092207, Accessed June 22, 2023.

[9] G. Haller, A. Hadjighasem, M. Farazmand, F. Huhn, Defining coherent vortices objectively from the vorticity. Journal of Fluid Mechanics, pp. 136–173, 2016.