Wall pressure and shear stress spectra from direct numerical simulations of turbulent plane channel flow are presented in this paper. Simulations have been carried out at a series of Reynolds numbers up to Re? = 1440, which corresponds to Re = 6:92 x 10(4) based on channel width and centerline velocity. Single-point and two-point statistics for velocity, pressure, and their derivatives have been collected, including velocity moments up to fourth order.§ The results have been used to study the Reynolds number dependence of wall pressure and shear stress spectra. It is found that the point spectrum of wall pressure collapses for Re? ? 360 under a mixed scaling for frequencies lower than the peak frequency of the frequency-weighted spectrum, and under viscous scaling for frequencies higher than the peak. Point spectra of wall shear stress components are found to collapse for Re? ? 360 under viscous scaling. The normalized mean square wall pressure increases linearly with the logarithm of Reynolds number. The rms wall shear stresses also increase with Reynolds number over the present range, but suggest some leveling off at high Reynolds number.

Wall Pressure and Shear Stress Spectra from Direct Simulations of Channel Flow

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The aerodynamic version amounts to a minor modification of a synthetic turbulence generator developed by the authors previously, but the acoustically adapted version is new and includes an internal damping layer, where the pressure field is computed by “weighting” of the instantaneous pressure fields from LES and RANS. This is motivated by the need to avoid creating spurious noise as part of the turbulence generation. In terms of pure aerodynamics, the validation includes canonical shear flows (developed channel flow, zero pressure gradient boundary layer, and plane mixing layer), as well as a more complex flow over the wall-mounted hump with non-fixed separation and reattachment, with emphasis on a rapid conversion from modeled to resolved Reynolds stresses. The aeroacoustic applications include the flow past a trailing edge and over a two-element airfoil configuration. In all cases the methodology ensures a very acceptable accuracy for the mean flow, turbulent statistics and, also, the near- and far-field noise.

Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems

4, in both internal (channel) and external (airfoil) flows. A review of the boundary-layer parameters characterizing the pressure gradient effects is provided, and the more relevant ones are introduced as new variables in the model. The method is then compared to the zero pressure gradient model it is derived from. The influence of the pressure gradient on the wall-pressure spectrum is discussed.Finally,themethodisappliedtoprovideinputdataofaradiatedtrailing-edge noisemodelbymeansofan aeroacoustic analogy, namely Amiet’s theory of turbulent boundary layer past a trailing edge. The results are compared to experimental data obtained in an open-jet anechoic wind tunnel.

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Wall-Pressure Spectral Model Including the Adverse Pressure Gradient Effects

Comparison of semi-empirical models for turbulent boundary layer wall pressure spectra

It is generally assumed that flows around wall-mounted sharp-edged bluff bodies
submerged in thick turbulent boundary layers are essentially independent of the
Reynolds number Re, provided that this exceeds some (2–3) × 104. (Re is based on
the body height and upstream velocity at that height.) This is a particularization of
the general principle of Reynolds-number similarity and it has important implications,
most notably that it allows model scale testing in wind tunnels of, for example,
atmospheric flows around buildings. A significant part of the literature on wind
engineering thus describes work which implicitly rests on the validity of this
assumption. This paper presents new wind-tunnel data obtained in the ‘classical’ case
of thick fully turbulent boundary-layer flow over a surface-mounted cube, covering an
Re range of well over an order of magnitude (that is, a factor of 22). The results are
also compared with new field data, providing a further order of magnitude increase in
Re. It is demonstrated that if on the one hand the flow around the obstacle does not
contain strong concentrated-vortex motions (like the delta-wing-type motions present
for a cube oriented at 45? to the oncoming flow), Re effects only appear on fluctuating
quantities such as the r.m.s. fluctuating surface pressures. If, on the other hand, the
flow is characterized by the presence of such vortex motions, Re effects are significant
even on mean-flow quantities such as the mean surface pressures or the mean velocities
near the surfaces. It is thus concluded that although, in certain circumstances and for
some quantities, the Reynolds-number-independency assumption is valid, there are
other important quantities and circumstances for which it is not.

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Bluff bodies in deep turbulent boundary layers: Reynolds-number issues

An empirical model of the surface pressure spectrum beneath a two-dimensional, zero-pressure-gradient boundary layer is presented that is based on the experimental surface pressure spectra measured by seven research groups. The measurements cover a large range of Reynolds number, 1.4 × 10 3 < Reθ < 2.34 × × 10 4 . The model is a simple function of the ratio of the timescales of the outer to inner boundary layer. It incorporates the effect of Reynolds number through the timescale ratio and compares well to experimental data. It is proposed that the effect of Reynolds number is more aptly described as the effect of the range of relevant scales. Spectral features of the experimental data and the scaling behavior of the surface pressure spectrum are also discussed.

Empirical Spectral Model of Surface Pressure Fluctuations

The mechanism for sound production from flow over a rough surface is not well understood. Measurements of radiated noise and low-wavenumber unsteady surface pressures were carried out in order to better understand the sound production mechanism. The initial results of an ongoing experimental investigation of the sound produced by flow over a rough surface are presented. In order to investigate scaling relationships, the flow speed, roughness height, and roughness element distribution were varied. Previous investigations have reported roughness noise levels that scale on flow velocity, roughness height, and fetch area and have indicated that the sound production may be dipole or quadrupole in nature. Prevailing analytical models assume that both types of sources are present. The scaling of roughness noise for large roughness height (k+ = uτ k/ν of order 1000) has not been investigated previously and is part of the current study. The scaling behavior of low-wavenumber surface pressures is discussed, in addition to the comparison of radiated noise spectra obtained by phased microphone array measurements.

Sound From Flow Over a Rough Surface

Sound produced by turbulent‐boundary layers (TBL) over rough walls is being studied in a series of physical‐computational experiments. At issue is the development of a knowledge of how the wall elements generate flow dipoles which directly determines how the sound is described in terms of dependent variables. The considered mechanisms include dipoles at the roughness elements due to their shed wakes, distributed surface dipoles due to convecting turbulence impinging onto elements, Rayleigh‐like scattering into sound of aerodynamic pressures of hydrodynamic wave numbers of flow above the roughness. The LES of rough‐wall TBL consists of "numerical" experiments being used to isolate the separate mechanisms. These simulations are benchmarked with analysis and with matching physical experiments on rough wall patches in which identical geometries of wall roughness and identical Reynolds numbers are used. In the physical measurements, array‐based measurements of the radiated sound are being used to characterize ...

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Investigations of roughness‐generated TBL sound using coupled physical‐computational experiments in conjunction with theoretical development

Unsteady Pressures on the Surface of a Ship Hull

Unsteady surface pressure measurements at locations distributed on the surface of a ship model hull and flow visualization of the bow wave and free surface are discussed. The measurements were performed in the David Taylor Model Basin using a ship model that is approximately 40 ft. long and representative of a naval combatant at Froude numbers from 0.14 to 0.44. The pressure measurement locations are distributed over the hull surface from 15 surface pressure spectrum and limited spatial coherence measurements are discussed. Additionally, the measured surface pressure spectra are compared to predictions done using an RANS‐based formulation and predictions done using an empirical formulation that is based on historical, flat‐plate, surface pressure spectra. [Work sponsored by Office of Naval Research, Code 334.]

Michael Goody

Papers

Empirical Spectral Model of Surface Pressure Fluctuations

Sound From Flow Over a Rough Surface

Investigations of roughness‐generated TBL sound using coupled physical‐computational experiments in conjunction with theoretical development

Unsteady Pressures on the Surface of a Ship Hull

Unsteady surface pressures on a ship hull