Modeling the Turbulence Spectrum Dissipation Range for Leading-Edge Noise Prediction

Abstract

Noise pollution caused by inflow turbulence is a major problem in many applications, e.g., propellers and fans. The Amiet leading-edge noise prediction model is widely applied in the design of silent propellers and fans, strongly relying on the accuracy of the inflow turbulence spectrum. The von Kármán energy spectrum accurately models the energy-containing range and inertial subrange of the turbulence spectrum. However, this model does not incorporate the dissipation range of the turbulent energy and leads to incorrect far-field noise estimates in the high-frequency range. In this study, empirical formulations are presented for the dissipation frequency and the dissipation range based on experimental data. Two passive grids were used to generate nearly isotropic inflow turbulence, which was characterized by hot-wire anemometry. These results showed that the dissipation frequency depends on the intensity of the velocity fluctuations and on the freestream velocity. The expressions proposed to predict the dissipation frequency and the dissipation range had a fairly good agreement with the measured data in this research and with experimental data from the literature. The predicted leading-edge noise is significantly affected by the dissipation range, causing a decrease in level of up to 17 dB for the highest frequencies.

On the turbulence distortion effects for airfoil leading-edge noise prediction

“…Two-component hot-wire measurements of turbulence quantities, spectra, and space-time correlations were performed for the grid without the airfoil in the flow. These measurements were discussed in [36]. These measurements showed that the turbulent flow is isotropic with a spectral form accurately described by the von Kármán turbulence spectrum.…”

“…and 𝑓 𝜂 is a formulation to model the dissipation range for high frequencies and 𝜂 is the Kolmogorov length scale. Dos Santos [36] proposed an empirical relation to model this term, see [36, pp. 8], and a formulation to compute the Kolmogorov length scale from turbulence parameters considering an isotropic turbulence [36, pp.…”

“…where 𝑓 𝑑 is the frequency that the dissipation range starts, i.e., the dissipation frequency. Dos Santos [36] showed that 𝑓 𝑑 depends on the flow speed, 𝑈, and 𝑢 𝑟 𝑚𝑠 following the expression [36, pp. 6]:…”

“…The frequency is nondimensionalized by the chord-based Strouhal number, 𝑆𝑡. The experimental turbulence spectrum is compared with the von Kármán and the RDT-based spectrum expressions combined with the dissipation range modeling proposed by dos Santos et al [36], Eqs. 7 and 9, respectively.…”

“…The high-frequency deviation is because the turbulence dissipation range for the TD case started at a lower frequency than for the NTD case. According to dos Santos [36], the frequency that the dissipation range starts, i.e., the dissipation frequency, 𝑓 𝑑 , depends on the flow speed, 𝑈, and 𝑢 𝑟 𝑚𝑠 following the expression in Eq. 6.…”