Study on the effect of leading and trailing-edge serrations on flat-plate broadband noise

Abstract

The results of a comparative study on the reduction of broadband noise for several combinations of a flat plate with serrations encountering a low-turbulence fluid flow are computed and documented. The four combinations under study are triangular serrations on leading-edge only, triangular serrations on trailing-edge only, triangular serrations on the leading and trailing edges, and ogival serrations on the leading and trailing edges. Serrations based on the trailing edge are normalized in terms of its chord length. A computational study was carried out using computational fluid dynamics models to simulate the variety of serrated flat plates. Commercial computational fluid dynamics software ANSYS Fluent 16.0 was used. A quantifiable reduction in the broadband noise was found in most of the variations in the serrated geometries. The particular case of the serrations considered in the present study having triangular serrations on both leading and trailing edges of the flat plate proved to be the most effective in terms of broadband noise reduction.

Keywords

Acoustics sound computational noise vibration

Introduction

Self-noise is the noise produced due to interaction of the fluid flow with a rigid surface. This noise is termed as airfoil self-noise in case of an airfoil. Trailing-edge noise is the main source of the self-noise generation mechanism.¹ Extensive research has been done to reduce noise generated at the trailing edge. The usage of serrations to reduce broadband noise is found to be one of the most effective ways as proved by Narayanan et al.² Some of the related research in literature is discussed in the following.

Moreau et al.³ conducted an experimental investigation to study the potential of noise reduction by a sawtooth trailing-edge serration on a flat plate. For the experiment, they varied the Reynolds number between the range $1.6 \times 10^{5} < (Re = ρ v d / υ) < 4.2 \times 10^{5}$ . Acoustic measurements were carried out for both serrated and sharp trailing edges in an anechoic wind tunnel. Due to the attenuation of vortex shedding, trailing-edge serrations were found to achieve reductions of up to 13 dB in the narrowband noise levels. The results showed that the noise reduction mechanism of trailing-edge serrations was dominated by their influence on hydrodynamic field at the source location. However, the assumption that the turbulent field is unaffected by the serrations may not be quite true for the type of configuration used here.

Gliebe⁴ analyzed that in a turbofan engine where fan blades were serrated such that the wakes produced by them, when mixed effectively leads to the attenuation of the fan noise. The fan blades were used for forced mixing of the rotor wakes to reduce the amplitude of wakes prior reaching the downstream stator vanes. The increase in the rate of mixing of the rotor wakes shed from the fan blades results in reduction of wake amplitude and turbulence levels at the stator vanes. The improved mixing characteristics, in turn, lead to improved engine efficiency.

Narayanan et al.² conducted an experimental investigation on the effects of serrations provided at the leading edge to reduce the broadband noise of a flat plate which was carried out in an open-jet wind tunnel. In comparison to a straight edge baseline flat plate, noise reduction was found to be significant in the mid-frequency range (500 Hz–8 kHz). Results were also compared with the noise reduction obtained on a serrated NACA-65 aerofoil having the same serration profile which was found to be significantly higher for the flat plate with a maximum noise reduction of around 9 dB compared with about 7 dB for the aerofoil. The serrations considered are in the form of sinusoidal profiles of wavelengths λ, and amplitude, 2h. It was also noted that the sound power reduction level was sensitive to the amplitude of the serration.

Herr and Dobrzynski⁵ summarized the results of an experimental study on the flow-permeable trailing-edge noise reduction using comb fiber serrations. The achievable noise reduction capability was quantified by directional microphone measurements on a flat plate and on a two-dimensional NACA0012-like airfoil in the open-jet aero-acoustic wind tunnel. An almost zero-spacing of the comb fibers (<0.1 mm) revealed the best results. This led to the assumption that the obtained noise reduction was mainly due to viscous damping of the turbulent flow pressure amplitude in the comb area. The tested trailing-edge modifications showed that uniform velocity scaling of the trailing-edge noise spectra was obtained. Therefore, the achievable noise reduction remained constant, irrespective of the flow velocity and the chord length.

The most popular methods used are direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged Navier–Stokes equation (RANS). DNS and LES approaches are computationally expensive. Hence, RANS approach is utilized for the present simulation.

Flat-plate geometries

Various design models simulated are as follows:

Baseline flat plate.

Flat plate with leading-edge triangular serrations.

Flat plate with trailing-edge triangular serrations.

Flat plate with single leading- and trailing-edge triangular serration.

Flat plate with leading- and trailing-edge triangular serrations.

Flat plate with leading- and trailing-edge ogival serrations.

All the designs are derived from the baseline flat plate which is of the same geometrical design as considered by Moreau et al.;⁶ therefore, they have the same chord, thickness, and span. The leading-edge serrations have aerodynamic drag penalties, while the trailing-edge serrations improved the reduction in the sound pressure level. Hence, the serrations are analyzed on both sides of the flat plate. The number serrations used on either edge for the various modified geometries is 90, and the serrated tips coincide with the edges of the flat plate. The equilateral triangular serration having base dimension 0.025 c and ogival serration having base dimension 0.025 c are depicted in Figure 1(a) and (b), respectively.

Figure1.

(a) Triangular serration and (b) ogival serration.

Acoustic model formulation

Lighthill acoustic analogy

Lighthill⁷ initiated a theory to estimate sound radiation from a fluid flow based on the equations of gas flow. Fluid flow over rigid boundaries results in flow fluctuations. Kinetic energy is converted into acoustic energy due to fluctuations in its momentum across rigid boundaries. Acoustic analogy equation was formulated by comparing fluid motion of sound propagation under static conditions. Equations are as follows

\frac{1}{c_{0}^{2}} \frac{\partial^{2} ρ^{'}}{\partial t^{2}} - \nabla^{2} ρ^{'} = \frac{\partial^{2} T_{i j}}{\partial x_{i} \partial x_{j}}

(1)

T_{i j} = ρ u_{i} u_{j} + P_{i j} - c^{2} ρ^{'} δ_{i j}

(2)

Here, ρ′ = ρ − ρ_o, where ρ′ is the density perturbation. T_ij is Lighthill’s stress tensor. P_ij = p′δ_ij − τ_ij is the compressive stress tensor where p′ and τ_ij are the fluctuating pressure and the total stress tensor, respectively. τ_ij = σ_ij − pδ_ij where σ_ij is the residual stress tensor and p is the pressure. Here, u_i and u_j are the velocity components in x_i and x_j directions, respectively, and c₀ is the speed of sound.

The first term of equation (2) represents unsteadiness of the fluid expressed in the quadruple source as Reynolds stress which is the turbulent-induced term. The second term is the dipole source due to local fluctuating stresses exerted by the surface on the fluid, and third term is the monopole source generated by mass flux fluctuating around the surface. To reduce the uncertainty on the sound pressure level, the computed fields were spatially averaged with respect to frequency.

Ffowcs Williams and Hawkings acoustic analogy

The differential form of Williams and Hawkings⁸ is as follows

\begin{array}{l} (\frac{\partial^{2}}{\partial t^{2}} - c_{0}^{2} \frac{\partial^{2}}{\partial x_{i}^{2}}) (H (f) ρ^{'}) = \frac{\partial^{2}}{\partial x_{i} \partial x_{j}} (T_{i j} H (f)) - \\ \frac{d F_{i} δ (f)}{d x_{i}} + \frac{d}{d t} (Q δ (f)) \end{array}

(3)

where $f$ is the surface of the body and is a function of f (x, t) = 0.

$f < 0$ represents inside of the body, whereas $f > 0$ represents outside of the body. Here, the right-hand side term is a source term

F_{i} = (P_{i j} + ρ ν_{i} (v_{i} - u_{j})) \frac{d f}{d x_{i}}

(4)

The last two terms in equation (4) are called loading noise

Q = (ρ_{o} u_{i} + ρ (v_{i} - u_{i})) \frac{d f}{d x_{i}}

(5)

The last two terms in equation (5) are called as thickness noise.

In equations (4) and (5), $u_{i}$ is the fluid velocity component in x_i direction and $v_{i}$ is the surface velocity component in x_i direction.

Computational details

The commercial software package ANSYS Fluent is used to solve the Ffowcs William and Hawkings equations to obtain the farfield noise. The computational study was conducted for baseline flat plate of a chord length c = 200 mm, thickness h = 0.025 c, and span s = 2.25 c at zero angles of attack. The radius of the circular leading edge is 0.0125 c. Trailing-edge apex angle is about 12°. Flat-plate geometry is enclosed inside a cuboidal geometry of dimension 1.575 c × 0.25 c × 3.75 c, and body is split into five parts as shown in the figure (Figure 2(a)) to incorporate fine mesh around it. An enclosure is created around the body which is a cube of dimension 6 c (Figure 2(b)) to incorporate coarse mesh. The second-order upwind spatial discretization scheme is used for the simulation which makes the solution difficult to converge at coarser grid size. But this type of scheme gives more accurate results than first-order upwind spatial discretization. The K-epsilon realizable viscosity model was used, which requires good resolution of the mesh near the walls for better prediction of the wall function.⁹

Figure 2.

(a) Two-dimensional computational domain, (b) cubical enclosure, and (c) boundary conditions of the model.

The CutCell assembly method is used for meshing. Accuracy of the solution depends on the number of elements used while meshing. Hence, to get satisfactory results, grid independency study of the domain is carried out. Grid-independent study also known as mesh convergence test is carried out to verify grid independent of the computational solution on size of the grid used while meshing.

Grid-independent study

The sensitivity of the grid to capture eddies accurately for noise measurement needs to be undertaken to reduce the computational time with accuracy. Hence, computational simulation is performed to compute the grid-independent study by varying the three different mesh sizes of 1,34,464; 1,60,000; and 3,95,689 elements.

It was found that the solution for domain with 1,60,000 and 3,95,689 mesh elements has higher order degree of accuracy with the experimental results as shown in Figure 3. Coarser grid of 1,34,464 elements could not capture the serration regions, leading to inaccuracy in the solution. The sound pressure level is plotted for the grids from which it can be found that the domain with 1.6 million elements agrees satisfactory with experimental results as shown in Figure 3.

Figure 3.

Mesh convergence study.

Average orthogonal quality of 0.98 was achieved for better convergence of the solution. A coarser mesh of size 0.375 c was used for the cubical fluid domain as shown in Figure 4(a). Element size near leading and trailing edges is given as 0.01125 c, while it is varying from 0.005 to 0.01 c everywhere else on the cuboid as shown in Figure 4(b).

Figure 4.

(a) Outer domain—coarse mesh. (b) Flat plate—fine mesh.

The boundary conditions of the model are shown in figure with the inlet as the velocity inlet with a turbulence intensity of 0.3% and the outlet boundary is pressure outlet. Other faces of the cubical fluid domain are considered as wall. No-slip boundary conditions are applied at the flat-plate surface. The inlet is provided with free stream velocity of 38 m/s with the Reynolds number of 5.20 × 10⁵ based on the chord length as considered in the present study. Computational simulation with unsteady, pressure-based solver was chosen to measure the sound pressure measurements. The viscous model used is K-epsilon, realizable, scalable wall function which incorporates a swirl-based correction reducing the turbulence for stability. Solution methodology is as follows: SIMPLE scheme for pressure-velocity coupling, second-order upwind spatial discretization, and second-order implicit transient formulation.

The Courant–Friedrichs–Lewy (CFL) number depends on the wave propagation velocity and on the cell size in the present simulations. Hence, the Courants number $C = u Δ t / Δ x$ (where u is the velocity magnitude, $Δ t$ is the timestep size, and $Δ x$ is the smallest mesh element size) is maintained below 1 which gives the timestep size of 0.0001 s with the current cell size.

Validation

Spectral distributions showing a variation of the sound pressure level (dB) with frequency (Hz) has been plotted and compared with the experimental results of Moreau et al.⁶ Computational simulation with Ffowcs Williams and Hawkings acoustic model agrees well with the experimental results (Figure 5). The trailing edge noise of airfoil¹⁰ at 102 m/s which is three times higher in speed than the present analysis is compared in similar parameters of the sound pressure level and frequency. It can be seen that the pressure spectrum levels are comparatively higher for the literature¹⁰ than the present due to the pressure fluctuations produced by the surface of the geometry.

Figure 5.

Validation with experimental results.

Results and discussion

The spectral plots obtained from the receivers up to 1000 Hz are plotted as shown in Figure 6. The comparison of the acoustical data obtained for all the cases under study along with the baseline flat plate clearly indicates that the flat plate with leading- and trailing-edge triangular serrations is the most effective giving rise to 60% reduction in the sound pressure level when compared with the baseline flat plate. The Ogival serrations also prove to reduce the sound pressure levels by 52%, but they are not as effective as the case of leading- and trailing-edge triangular serrations. The results are summarized in Table 1.

Figure 6.

Comparison of acoustic results.

Table 1.

Acoustical data for the models considered in the present study.

Flat-plate configuration	Overall sound pressure level (dB)	Reduction in the overall sound pressure level (dB)	Percentage of reduction in the overall sound pressure level (%)
Baseline flat plate	62	–	–
Flat plate with leading-edge triangular serrations	45	17	27
Flat plate with trailing-edge triangular serrations	35	27	44
Flat plate with leading- and trailing-edge triangular serrations	25	37	60
Flat plate with leading- and trailing-edge ogival serrations	27	32	52

The velocity contours for all the flat plates were obtained and depicted in Figure 7(a)–(e). It can be seen that there is maximum stagnation of fluid flow at the edges of the baseline flat plate, and this stagnation tends to reduce with each variation of the serrated flat plates. To reduce the stagnation of fluid flow, the serrations need to be introduced on leading and trailing edges of the baseline flat plate.

Figure 7.

(a) Velocity contours for the baseline flat plate, (b) velocity contours for the flat plate with leading-edge triangular serration, (c) velocity contours for the flat plate with trailing-edge triangular serration, (d) velocity contours for the flat plate with leading- and trailing-edge triangular serrations, and (e) velocity contours for the flat plate with leading- and trailing-edge ogival serrations.

The velocity component increases from the leading edge toward the trailing edge with increasing the acceleration along with boundary layer thinning effect. The flow starts to accumulate in the serration space as observed by the decrease in the velocity gradient from Figure 7(d). The flow starts to flow in the outward direction leading to the increase in velocity along the spanwise direction. From Figure 7(e), it can be seen that the curve shape of the ogival configuration delays the outward and downward flow direction. The triangular serrations have sharp tip, while ogival has curve which reduces the strong upwash generated by the flow due to the mixing of vortices from the edges of the serrations. The near-wall distortions for the leading-edge triangular serrations reduce the overall sound pressure level by a margin of 10% compared with the leading edges of ogival shape serrations.

Conclusion

A comparative computational study on effect of serrations to reduce aerodynamic self-noise of the flat-plate simulations was carried out using commercial software ANSYS Fluent. The Reynolds number considered was 5.20 × 10⁵. Flat plate with triangular serration at leading and trailing edges is found to be more effective by 52% than without serrations. Separately, it was also found that triangular serrations are more effective than ogival serrations. Further optimized investigation can be undertaken on other different types of serrations to identify the shape which will be most effective for noise reduction.

Footnotes

Acknowledgements

The authors wish to acknowledge the contribution of Fluid Dynamics High-Performance Computing (SIMULIA) facilities made available in the campus to carry out the present research. The software package FLUENT^® 16.0 is provided by ANSYS for research students is greatly appreciated.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

GC Vishnu Kumar

References

Brooks

Pope

Marcolini

. Airfoil self-noise and prediction. NASA reference publication 1218, 1989. Washington, DC: NASA.

Narayanan

Chaitanya

Haeri

, et al. Airfoil noise reductions through leading-edge serrations. Phys Fluids 2015; 27(2): 025109.

Moreau

Doolan

. Noise-reduction mechanism of a flat-plate serrated trailing edge. AIAA J 2013; 51(10): 2513–2522.

Gliebe

. Serrated fan blade. Patent US 6,733,240 B2, USA, 2004.

Herr

Dobrzynski

. Experimental investigations in low-noise trailing-edge design. AIAA J 2005; 43(6): 1167–1175.

Moreau

Brooks

Doolan

. Empirical study of flat plate trailing edge flow and noise. In: Proceedings of the fourteenth Australian international aerospace congress (AIAC14), Melbourne, VIC, Australia, 28 February–3 March 2011.

LightHill

. On sound generated aerodynamically I. General theory. P Roy Soc Lond A Mat 1952; 211(1107): 564–587.

Williams

Hawkings

. Sound generation by turbulence and surfaces in arbitrary motion. Philos T R Soc A 1969; 264(1151): 321–342.

Avallone

van der Velden

Ragni

. Benefits of curved serrations on broadband trailing-edge noise reduction. J Sound Vib 2017; 400: 167–177.

10.

Amiet

. Noise due to turbulent flow past a trailing edge. J Sound Vib 1976; 47(3): 387–393.