Julio Soria

Abstract: Numerical differencing schemes are subject to dispersive a nd dissipative errors, which in one dimension are functions of wavenumber. When these schemes are applied in two or three dimensions, the errors become functions of both wavenumber and the direction of wave propagation. In this paper spectra l analysis was used to analyse the magnitude and direction in error of the group velocity of vorticity-entropy and acoust ic waves in the solution of the linearised Euler equations in a t wodimensional Cartesian space. The anisotropy in these error s for three schemes were studied as a function of the wavenumber, wave direction, mean flow direction and mean flow Mach number. It was found that the traditional measure of error the r atio of the magnitudes of the numerical to real group velocities does not accurately capture the total error for waves which a re traveling in an oblique direction to the mean flow. Therefore a second measure of a scheme’s error that better represents t h total error in the scheme is presented. Numerical experimen ts were run to provide confirmation of the developed theory. Introduction With increased interest in the computation of turbulence an d with the advent of computational aeroacoustics (CAA), meth ods were developed to increase the resolution of finite diffe rence schemes as required for these applications. Formal tru ncation error provides some indication of the accuracy of a nu merical scheme; however, far more information can be obtain ed from a spectral analysis in which one can identify the resolv able wavenumbers. The use of spectral analysis to assess the resolution of numerical schemes is well established ([7] an d [15]). However, the overwhelming majority of analyses on the resolution and accuracy of these schemes have been performed in only one dimension. In some cases schemes were tested for their performance in two dimensions [4, 5, 1, 2, 3] , whilst others have anisotropy reduction as a primary motiva tion [6, 8, 9, 11, 13, 16]. In most cases the analysis of anisotropy in a scheme’s error is portrayed by a polar plot of the ratio of num erical phase speed to exact phase speed for a range of wavenumbers. Implicit in such an analysis is the assumption that the waves are aligned with the direction of propagation. This as sumption is restrictive and does not apply in general applic ations. [14] showed how the physical propagation of the waves moves according to group velocity and [12, p.558] asserts th at phase velocity is ’totally irrelevant’ with regards to the e rror of wave propagation. Therefore this paper focuses on the use of group velocity to explain the phenomena observed. For the pu rposes of exploring the anisotropy of finite difference schem es the sixth order central difference scheme (CDS6) is used as a n example. The definition of the CDS6 scheme and its equivalent wavenumber as a function of actual wavenumber is commonly found in literature (e.g. [8]) and will not be explicitly defi ned here. This paper provides an overview of the work found in [10]. Definition of Error Measures From the linear evolution form of the Euler equations ∂U ′ ∂t +A1 ∂U ′ ∂x1 +A2 ∂U ′ ∂x2 = 0, (1)

Abstract: Methodologies for the experimental measurement of threedimensional instantaneous density fluctuations via tomographic background-oriented schlieren (TBOS) were assessed using synthetic background images, corresponding to experimental measurements of a heated turbulent jet. Filtered back projection and iterative algebraic reconstruction algorithms were explored. Results show a superior reconstruction when the solutions from filtered back projection were used as an initial solution to a masked and windowed iterative algebraic reconstruction. The influence of the number of cameras and the wavelength of density fluctuations are both investigated.

TL;DR: In this article, the accuracy of the digital in-line holography in the 90 o scattering recording configuration using a previously characterized turbulent jet flow was quantified using the Reynolds number based on the mean velocity and diameter at the nozzle exit is in the range of 3,000 6,000.

TL;DR: In this paper, an investigation by 2D-2C particle image velocimetry was carried out in the far downstream section (greater than 70 downstream boundary layer thicknesses, δ 99 measured in the region of interest) of a nominally zero pressure gradient 0.5m square re-circulating water tunnel seeded with 11∝m Potter's hollow glass spheres.