Analytical reconstruction of isotropic turbulence spectra based on the Gaussian transform. (25th June 2016)

• Record Type: Journal Article
• Authors: Wohlbrandt, A.; Hu, N.; Guérin, S.; Ewert, R.
• Is Part Of: Computers & fluids. Volume 132(2016)
• Page Start: 46
• Page End: 50
• Publication Date: 2016-06-25
• Subjects: Isotropic turbulence -- Broadband noise simulation -- Gaussian filter -- Gaussian transform -- Von Karman and Liepmann spectra -- Fast Random-Particle-Mesh method; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2016.03.023
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Realisation of isotropic turbulence spectra by analytically superposing Gaussian spectra. Analytical derivation of the weighting function for von Karman and Liepmann spectra. Discretisation and truncation for a small number of Gaussian spectra. Validation on the example of a turbulence velocity von Karman spectrum. Abstract: The field of application of the Random Particle Mesh (RPM) method used to simulate turbulence-induced broadband noise in several aeroacoustic applications is improved to realise isotropic turbulence spectra. With this method turbulent fluctuations are synthesised by filtering white noise with a Gaussian filter kernel that in turn gives a Gaussian spectrum. The Gaussian filter is efficient and finds wide-spread applications in stochastic signal processing. However Gaussian spectra do not correspond to real turbulence spectra. Thus in turbo-machines the von Kármán, Liepmann, and modified von Kármán spectra are more realistic model spectra. In this note we analytically derive weighting functions to realise arbitrary isotropic solenoidal spectra using a superposition of weighted Gaussian spectra of different length scales. The analytic weighting functions for the von Kármán, the Liepmann, and the modified von Kármán spectra are derived subsequently. Finally a method is proposed to discretise the problem using a limited number of Gaussian spectra. The effectivity of this approach is demonstrated by realising a von Kármán velocity spectrum using the RPM method.