Showing papers by "Neil D. Sandham published in 2006"

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

Abstract: 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.

Effect of Mach number on the structure of turbulent spots

Abstract: Direct numerical simulations have been performed to study the dynamics of isolated turbulent spots in compressible isothermal-wall boundary layers. Results of a bypass transition scenario at Mach 2, 4 and 6 are presented. At all Mach numbers the evolved spots have a leading-edge overhang, followed by a turbulent core and a calmed region at the rear interface. The spots have an upstream-pointing arrowhead shape when visualized by near-wall slices, but a downstream-pointing arrowhead in slices away from the wall. The lateral spreading of the spot decreases substantially with the Mach number, consistent with a growth mechanism based on the instability of lateral shear layers. Evidence for a supersonic (Mack) mode substructure is found in the Mach 6 case, where coherent spanwise structures are observed under the spot overhang region.

Nonlinear mechanisms of sound generation in a perturbed parallel jet flow

Abstract: An initial value problem with relevance to jet noise is investigated. A plane parallel jet flow is subjected to a spatially localized initial disturbance and is then left to evolve according to the two-dimensional compressible Navier–Stokes equations. The hydrodynamic response is in the form of a convecting vortex packet. The Ffowcs Williams–Hawkings approach is formulated in the time domain and used to extrapolate from the simulated near field to the acoustic far field. The predominant downstream sound radiation comes from an early stage of nonlinear development of the vortex packet. Two simplified models to account for the radiation are introduced, based on nonlinear mode interactions on a prescribed base flow. The first uses two sets of linearized Euler equations, coupled via the inviscid Lilley–Goldstein acoustic analogy. This formulation separates the linear sound field from the sound field driven by nonlinear interactions; qualitative agreement of the latter with the Navier–Stokes computations demonstrates the importance of nonlinear interactions. The second model uses combinations of linear inviscid eigenmodes to drive the sound field, which allows extraction of the dominant mode interactions responsible for the observed radiation pattern. The results indicate that a difference-wavenumber nonlinear interaction mechanism dominates sound radiation from subsonic instability modes in shear flows.

Sound radiation from a turbulent boundary layer

Abstract: Sound radiation due to fluctuating viscous wall shear stresses in a plane turbulent boundary layer is investigated by a two-stage procedure using direct numerical simulation (DNS) databases for incompressible turbulent Poiseuille flow in a plane channel, at Reynolds numbers up to Reτ=1440. The power spectral density of radiated pressure and spectra of sound power per unit wall area are calculated in the low Mach number limit by substituting source terms obtained from DNS into a Ffowcs Williams–Hawkings wave equation and using a half-space Green function. The same DNS data are used to predict the spectrum of turbulent boundary layer noise measured in a diffuser downstream of a fully developed channel flow [Greshilov and Mironov, Sov. Phys. Acoust. 29, 275 (1983)]. The measured spectrum is ∼15dB higher at low frequencies, but converges with the prediction at high frequencies.

A zonal characteristic boundary condition for numerical simulations of aerodynamic sound (eccomas cfd 2006)

Abstract: This paper presents a non-re∞ecting boundary condition that signiflcantly reduces the spurious pressure oscillations that are produced when vortical structures in a compressible ∞ow cross the computational farfleld boundaries. The method is based on commonly used characteristic boundary conditions. Here, incoming characteristics are ramped to zero in a bufier region as opposed to merely setting them to zero at the boundary. One of the key features of the approach is that it is free of coe-cients requiring calibration. The equivalence of two formulations of the zonal boundary condition is verifled with a model problem. Direct numerical simulations of trailing edges at difierent Mach numbers are conducted to demonstrate the efiectiveness of the novel approach.

A zonal characteristic boundary condition for numerical simulations of aerodynamic sound

Abstract: This paper presents a non-reflecting boundary condition that significantly reduces the spurious pressure oscillations that are produced when vortical structures in a compressible flow cross the computational farfield boundaries. The method is based on commonly used characteristic boundary conditions. Here, incoming characteristics are ramped to zero in a buffer region as opposed to merely setting them to zero at the boundary. One of the key features of the approach is that it is free of coefficients requiring calibration. The equivalence of two formulations of the zonal boundary condition is verified with a model problem. Direct numerical simulations of trailing edges at different Mach numbers are conducted to demonstrate the effectiveness of the novel approach.

Analysis of Data on the Relation between Eddies and Streaky Structures in Turbulent Flows Using the Placebo Method

Abstract: An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed.

Turbulent spots in a compressible boundary-layer flow

Abstract: Direct simulation of an isolated turbulent spot in a compressible isothermal wall boundary-layer flow has been performed. A bypass transition scenario at Mach 2,4 and 6 is considered. The flow field associated with the transitional and turbulent spots is studied in detail, with results in broad agreement with previous experimental work. The evolved spots are found to have an arrowhead shaped front with a leading edge overhang, followed by a turbulent core and a calmed region at the rear interface. The lateral spreading of the spot is found to decrease substantially with the flow. Evidence for a supersonic (Mack) mode is found in the Mach 6 case: spanwise-coherent structures are observed under the spot overhang region.

DNS of trailing-edge noise generated by boundary-layer instabilities

Abstract: Direct numerical simulations (DNS) are conducted of noise generated at an infinitely thin trailing edge (TE). The aim is to predict the far-field sound and the near-field hydrodynamics, providing an insight into the physical mechanisms of sound generation and potentially helping to validate acoustic theories. In particular, the DNS data are compared with Amiet's theory, where the farfield sound can be evaluated in closed form if the convecting surface pressure spectrum upstream of the TE is known. For the present investigation, Tollmien-Schlichting waves are introduced close to the inflow boundary. The disturbances propagate downstream producing pressure fluctuations at the TE. In conducting two-dimensional DNS the theoretical method requires modification to account for the radiation of the total pressure difference in two dimensions only, as opposed to the three dimensional sound radiation originally considered by Amiet. For DNS, a high-order accurate numerical method is chosen which is free of upwinding, artificial dissipation or any form of explicit filtering, and employs a novel boundary treatment. The modified theoretical analysis and a comparison between DNS and theoretical results are presented, scrutinizing the assumptions made in the derivation. Amiet's surface pressure jump transfer function is found to predict the scattered pressure field accurately. Directivity plots of DNS data show that viscous effects appear to smear individual lobes and that a strong downstream pointing lobe is present which is attributed to an additional wake source.

Direct numerical simulation of the flow around an airfoil with unsteady wake

Abstract: Direct numerical simulations of a NACA-0012 airfoil at zero degrees incidence are presented for a range of Mach and Reynolds numbers. At Reynolds number 10,000, the flow around the airfoil is found to be dominated by vortex shedding from an unstable wake. Frequencies are found to collapse using a Strouhal number based on trailing edge displacement thickness, while amplitude increases with Mach number. At Reynolds number 50,000, vortex shedding from an unstable wake is again present. At certain Mach numbers an additional low-frequency large-amplitude mode of oscillation is observed. Behaviour of the upper and lower boundary layers, as well as the local fluid properties, is described over the course of the low frequency cycle. The onset of the low frequency oscillation is mapped in terms of Reynolds and Mach numbers.

Noise due to unsteady flow past trailing edges (eccomas cfd 2006)

Abstract: This paper presents two-dimensional direct numerical simulations (DNS) of noise generated at trailing edges (TE) with zero thickness. The simulations are conducted specifying either no-slip or slip walls in order to investigate viscous efiects. In both cases, small amplitude disturbances are introduced close to the in∞ow boundary that serve as pressure disturbances at the TE. DNS data reveals that the unsteady Kutta condition is not satisfled, irrespective of the wall boundary condition. However, it appears that the va- lidity of the unsteady Kutta condition is not essential for making an accurate prediction of the far fleld noise. The far fleld pressure is predicted as a function of the surface pressure difierence using a 2-D modiflcation of Amiet's classical theory, and compared with the far fleld pressure computed directly. Directivity plots provide evidence that the presence of boundary layers and noise generated by an unsteady wake in the no-slip cases lead to smearing of individual lobes, and that the downstream pointing lobes in no-slip wall cases are probably due to nonlinear noise generation in the wake. The simulations are con- ducted using a high-order accurate numerical method which is free of upwinding, artiflcial dissipation or any form of explicit flltering, and employs a novel boundary treatment.

Noise due to Unsteady Flow Past Trailing Edges

Abstract: This paper presents two-dimensional direct numerical simulations (DNS) of noise generated at trailing edges (TE) with zero thickness. The simulations are conducted specifying either no-slip or slip walls in order to investigate viscous effects. In both cases, small amplitude disturbances are introduced close to the inflow boundary that serve as pressure disturbances at the trailing edge. DNS data reveals that the unsteady Kutta condition is not satisfied, irrespective of the wall boundary condition. However, it appears that the validity of the unsteady Kutta condition is not essential for making an accurate prediction of the far field noise. The far field pressure is predicted as a function of the surface pressure difference using a 2-D modification of Amiets classical theory, and compared with the far field pressure computed directly. Directivity plots provide evidence that the presence of boundary layers and noise generated by an unsteady wake in the no-slip cases lead to smearing of individual obes, and that the downstream pointing lobes in no-slip wall cases are probably due to nonlinear noise generation in the wake. The simulations are conducted using a high-order accurate numerical method which is free of upwinding, artificial dissipation or any form of explicit filtering, and employs a novel boundary treatment.

Direct numerical simulation of an airfoil with unsteady wake (eccomas 2006)

Abstract: Direct numerical simulations of a NACA-0012 airfoil at zero degrees incidence are presented for a range of Mach and Reynolds numbers. At Reynolds number 10,000, the flow around the airfoil is found to be dominated by vortex shedding from an unstable wake. Frequencies are found to collapse using a Strouhal number based on trailing edge displacement thickness, while amplitude increases with Mach number. At Reynolds number 50,000, vortex shedding from an unstable wake is again present. At certain Mach numbers an additional low-frequency large-amplitude mode of oscillation is observed. Behaviour of the upper and lower boundary layers, as well as the local fluid properties, is described over the course of the low frequency cycle. The onset of the low frequency oscillation is mapped in terms of Reynolds and Mach numbers.

Prediction of boundary layer sound radiation from wall shear stresses using DNS data

Abstract: Sound radiation from a plane turbulent boundary layer is investigated using databases from direct numerical simulations (DNS) of plane turbulent Poiseuille flow up to Reynolds number Re? = 1440. Correlation areas for fluctuating wall shear stresses are found to collapse on viscous scaling over the current Reynolds number range. The power spectral density of radiated pressure and the spectrum of radiated sound power, per unit wall area, are predicted in the low Mach number limit by solving a Ffowcs Williams–Hawkings type wave equation using a half-space Green function. The same DNS data are used to predict the spectrum of turbulent boundary layer noise measured in a diffuser downstream of a fully-developed channel flow [Greshinov & Mironov, Soviet Physics Acoustics, 29(4):257-280,1983]. The measured spectrum is higher at low frequencies, but converges with the prediction at high frequencies.

Evaluation of acoustic sources in an excited unstable laminar shear layer

Abstract: The radiation of sound from artificial sources in a developing shear layer is studied numerically, in order to address an issue that arises in acoustic analogy models of jet noise: namely whether the unstable response of the mean-flow shear layer has a significant effect on sound radiation. Direct numerical simulation of a forced two-dimensional compressible laminar mixing layer has been carried out at a Reynolds number of 250, based on the mixing layer initial vorticity thickness and the upper free-stream velocity. The free-stream Mach numbers of the mixing layer are 0.9 and 0.45. The flow is excited with a single-frequency body force field that is acoustically compact and is derived from an applied-stress distribution. Sound radiation from the mixing layer is calculated at the forcing frequency, and compared with radiation from a uniform flow under the same forcing. Comparisons are shown for the most-unstable forcing frequency over a wide amplitude range. The pressure radiated on either side of the mixi...