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L ehrstuhl für Modellierung und Simulation Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory.

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Presentation on theme: "L ehrstuhl für Modellierung und Simulation Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory."— Presentation transcript:

1 L ehrstuhl für Modellierung und Simulation Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory of turbulence Lecture 3 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

2 Basic definitions. Reynolds averaging 2 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

3 3 Basic definitions. Correlation function Correlation function Correlation function in homogeneous turbulence Autocorrelation function Integral length Autocorrelation temporal function Integral time UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

4 Samples 4 50 mm Resolution 300 µ 2D A B C A B C Typical form of the autocorrelation coefficient. Scalar turbulence PLIF Measurements of the LTT Rostock Physical meaning of sign change UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

5 Samples 5 50 mm Resolution 300 µ 2D Typical distribution of the integral length along the jet mixer. Scalar turbulence PLIF Measurements of the LTT Rostock UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

6 Typical autocorrelation coefficient along the jet 6 (from Ginevsky et al. (2004) Acoustic control of turbulent jets. Springer) UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION 1 along upper border of nozzle at x/D=0.5 2 along the jet axis at x/d=3.0 autocorrelation coefficient of the longitudinal velocity

7 Isotropic turbulence 7 UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

8 8 Taylor longitudinal length Taylor transverse length Taylor Reynolds number Isotropic turbulence UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

9 Correlation function in Fourrier space 9 Usually it is possible to measure only the One dimensional spectral Function UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

10 Proof 10UNIVERSITÄT ROSTOCK | LEHRSTUHL FÜR Modellierung und SIMULATION

11 Spectral density of the kinetic energy 11 E(k) dk is the contribution of oscillations with the wave numbers k { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/1/634969/slides/slide_11.jpg", "name": "Spectral density of the kinetic energy 11 E(k) dk is the contribution of oscillations with the wave numbers k


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