3 results
Three-dimensional effects on the transfer function of a rectangular-section body in turbulent flow
- Yang Yang, Mingshui Li, Haili Liao
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- Journal:
- Journal of Fluid Mechanics / Volume 872 / 10 August 2019
- Published online by Cambridge University Press:
- 10 June 2019, pp. 348-366
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This paper investigates the influence of three-dimensional effects on the transfer function of a rectangular-section body in turbulent flow. The dimensionless factor $\unicode[STIX]{x1D713}$, as derived by Li et al. (J. Fluid Mech., vol. 847, 2018, pp. 768–785), is adapted to evaluate this influence. The calculation of $\unicode[STIX]{x1D713}$ requires the spanwise influence term. For this purpose, an adapted form of the lift coherence function is derived, enabling the use of the measured lift coherence for the estimation of the spanwise influence term. Three rectangular models with different cross-sections (chord-to-depth ratios of 3, 5 and 10) are chosen for testing, and a NACA 0015 airfoil model is tested for comparison. Using the measured spanwise influence terms, the dimensionless factors of these models are then numerically calculated under different ratios of the turbulent integral scale to the chord $\unicode[STIX]{x1D6FE}$ and aspect ratios $\unicode[STIX]{x1D703}$. It is shown that the dimensionless factors of the rectangular models increase as $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D703}$ increase, which are similar to the dimensionless factor of the airfoil model. If $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D703}$ have suitable values, the strip theory could be applicable to the rectangular-section body. It is also found that the dimensionless factors of all the rectangular models are larger than the dimensionless factor of the airfoil model under the same parameters. The smaller the chord-to-depth ratio is, the larger the dimensionless factor is. Using the strip theory to calculate the lift response of the rectangular-section body may provide more accurate estimation. Additionally, the one-wavenumber transfer functions of these models are determined under the consideration of the three-dimensional effects. The results show that the experimental transfer functions of the rectangular models cannot be captured by the Sears function. They are larger than the Sears function at lower frequencies, while falling at a faster rate as the frequency increases. For bluff bodies with separated flow, the modified transfer function presented here appears to be an appropriate approach.
Direct measurement of the Sears function in turbulent flow
- Mingshui Li, Yang Yang, Ming Li, Haili Liao
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- Journal:
- Journal of Fluid Mechanics / Volume 847 / 25 July 2018
- Published online by Cambridge University Press:
- 29 May 2018, pp. 768-785
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The applicability of the strip assumption in the estimation of the unsteady lift response of a two-dimensional wing in turbulent flow is investigated. The ratio between the lift spectrum calculated from the two-wavenumber analysis and the lift spectrum calculated from the strip assumption is used to evaluate the accuracy of the strip assumption. It is shown that the accuracy of the strip assumption is controlled by the ratio of the turbulence integral scale to the chord and the aspect ratio. With an increase of these two parameters, the ratio for evaluating the accuracy of the strip assumption increases, the one-wavenumber transfer function obtained from the strip assumption approaches the Sears function gradually. When these two parameters take suitable values, the strip assumption could be applicable to the calculation of the unsteady lift on a wing in turbulent flow. Here, the term aspect ratio refers to the ratio of the specified span (an finite spanwise length of the two-dimensional wing) to the chord, the unsteady lift is calculated over this specified spanwise length. The theoretical analysis is verified by means of force measurement experiments conducted in a wind tunnel. In the experiment, a square passive grid is installed downstream of the entrance of the test section to generate approximately homogeneous and isotropic turbulence. Three rectangular wings with different aspect ratios ($\unicode[STIX]{x1D703}=3$, 5 and 7) are used. These wing models have an NACA 0015 profile cross-section and a fixed chord length $c=0.16~\text{m}$. The testing results show that, at a fixed ratio of turbulence integral scale to chord, the deviation between the experimental one-wavenumber transfer function obtained from the strip assumption and the Sears function is reduced with increasing aspect ratio, as expected by the theoretical predictions. However, due to the effect of thickness, the experimental values at high frequencies cannot be captured by the Sears function which is derived based on the flat plate assumption. In practical applications, the effect of thickness on the transfer function should be considered.
The lift on an aerofoil in grid-generated turbulence
- Shaopeng Li, Mingshui Li, Haili Liao
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- Journal:
- Journal of Fluid Mechanics / Volume 771 / 25 May 2015
- Published online by Cambridge University Press:
- 14 April 2015, pp. 16-35
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The three-dimensional effects of turbulence cannot be neglected when the spanwise wavelength of the incident turbulence is not effectively infinite with respect to the chord, which may invalidate the strip assumption. Based on three-dimensional theory, a general approach, expressed in terms of a two-dimensional Fourier transform of the correlation of the buffeting force, is proposed to identify the two-wavenumber spectrum and aerodynamic admittance of the lift force on an aerofoil. It is essential that the approach presented can be validated in wind tunnel experiments. The coherence of the lift force on an aerofoil in grid-generated turbulence is obtained by simultaneous measurements of unsteady surface pressures around several chordwise strips on a stiff sectional model, which controls the accuracy of results. For the purpose of the Fourier transform, three empirical coherence models of the lift force are presented to fit the experimental results. Compared with the linearized theory, the two-wavenumber aerodynamic admittance can describe well the pressure distribution and the pattern of energy transition in an isotropic turbulence field. Thus, the failure mechanism of the traditional strip assumption can be demonstrated explicitly. In addition, the results obtained also validate the theory proposed by Graham (Aeronaut. Q., vol. 21, 1970, pp. 182–198; Aeronaut. Q., vol. 22, 1971, pp. 83–100). The present approach can be extended to study the three-dimensionality of the buffeting force on line-like structures with arbitrary cross-configurations, such as long-span bridges and high-rise buildings.