A modification of Amiet's classical trailing edge noise theory for strictly two dimensional flows

The aim of this report is to derive theoretical expressions for the far-field pressure generated by disturbances convecting over a trailing edge. First, a general calculation of thefar-field pressure is discussed. Then the classical theory of Amiet (1976b) is reviewed,listing the most relevant assumptions. Amiet's theory is then revised for two-dimensional flows

Viscous instability of a compressible round jet

The compressible linear stability equations are derived from the Navier Stokes equations in cylindrical polar coordinates. Numerical solutions for locally parallel flow are found using a direct matrix method. Discretization with compact finite difference is found to have better convergence properties than a Chebyshev spectral method for a round jet test case. The method is validated against previous results and convergence is tested for a range of jet profiles. Finally and en method is used to determine the dominant frequency of a Mach 0.9 jet

Direct numerical simulation of turbulent flow over a rough surface based on a surface scan

Typical engineering rough surfaces show only limited resemblance to the artificially constructed rough surfaces that have been the basis of most previous fundamental research on turbulent flow over rough walls. In this article flow past an irregular rough surface is investigated, based on a scan of a rough graphite surface that serves as a typical example for an irregular rough surface found in engineering applications. The scanned map of surface height versus lateral coordinates is filtered in Fourier space to remove features on very small scales and to create a smoothly varying periodic representation of the surface. The surface is used as a no-slip boundary in direct numerical simulations of turbulent channel flow. For the resolution of the irregular boundary an iterative embedded boundary method is employed. The effects of the surface filtering on the turbulent flow are investigated by studying a series of surfaces with decreasing level of filtering. Mean flow, Reynolds stress and dispersive stress profiles show good agreement once a sufficiently large number of Fourier modes are retained. However, significant differences are observed if only the largest surface features are resolved. Strongly filtered surfaces give rise to a higher mean-flow velocity and to a higher variation of the streamwise velocity in the roughness layer compared with weakly filtered surfaces. In contrast, for the weakly filtered surfaces the mean flow is reversed over most of the lower part of the roughness sublayer and higher levels of dispersive shear stress are found

Sound radiation in turbulent channel flows

Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit

Surface-sampled simulations of turbulent flow at high Reynolds number

A new approach to turbulence simulation, based on a combination of large-eddy simulation (LES) for the whole flow and an array of non-space-filling quasi-direct numerical simulations (QDNS), which sample the response of near-wall turbulence to large-scale forcing, is proposed and evaluated. The technique overcomes some of the cost limitations of turbulence simulation, since the main flow is treated with a coarse-grid LES, with the equivalent of wall functions supplied by the near-wall sampled QDNS. Two cases are tested, at friction Reynolds number Re$_\tau$=4200 and 20,000. The total grid node count for the first case is less than half a million and less than two million for the second case, with the calculations only requiring a desktop computer. A good agreement with published DNS is found at Re$_\tau$=4200, both in terms of the mean velocity profile and the streamwise velocity fluctuation statistics, which correctly show a substantial increase in near-wall turbulence levels due to a modulation of near-wall streaks by large-scale structures. The trend continues at Re$_\tau$=20,000, in agreement with experiment, which represents one of the major achievements of the new approach. A number of detailed aspects of the model, including numerical resolution, LES-QDNS coupling strategy and sub-grid model are explored. A low level of grid sensitivity is demonstrated for both the QDNS and LES aspects. Since the method does not assume a law of the wall, it can in principle be applied to flows that are out of equilibrium.Comment: Author accepted version. Accepted for publication in the International Journal for Numerical Methods in Fluids on 26 April 201

Reynolds number dependence of the near-wall flow over irregular rough surfaces

The database contains representations of the two surfaces studied, a graphite and a gritblasted surface, and the corresponding time-averaged velocity data for Reynolds numbers Re� = 90; 120; 180; 240; 360; 540, and 720