Basic definitions . Reynolds averaging

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# Basic definitions . Reynolds averaging - PowerPoint PPT Presentation

Statistical theory of the isotropic turbulence (K-41 theory) 1. Basic definitions of the statistical theory of turbulence Lecture 3. Basic definitions . Reynolds averaging. Basic definitions . Correlation function. Correlation function Correlation function in homogeneous turbulence

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### Statistical theory of the isotropic turbulence (K-41 theory)1. Basic definitions of the statistical theory of turbulenceLecture 3

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Basic definitions. Reynolds averaging

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Basic definitions. Correlationfunction

Correlationfunction

Correlationfunction in homogeneous

turbulence

Autocorrelationfunction

Integral length

Autocorrelation temporal function

Integral time

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Samples

Resolution 300 µ

50 mm

2D

Typical form oftheautocorrelationcoefficient. Scalarturbulence

B

A

C

A

B

C

Physicalmeaningofsignchange

PLIF Measurementsofthe LTT Rostock

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Samples

Resolution 300 µ

50 mm

2D

Typicaldistributionofthe integral lengthalongthejetmixer.

Scalarturbulence

PLIF Measurementsofthe LTT Rostock

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Typicalautocorrelationcoefficientalongthejet

autocorrelationcoefficientofthe

longitudinal velocity

1 alongupperborderofnozzleat x/D=0.5

2 alongthejetaxisat x/d=3.0

(fromGinevsky et al. (2004) Acoustic control of turbulent jets. Springer)

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Isotropicturbulence

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Isotropic turbulence

Taylor longitudinal length

Taylor transverselength

Taylor Reynolds number

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Correlationfunction in Fourrierspace

Usuallyitispossibletomeasureonlythe

„One dimensional spectralFunction“

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

Proof

UNIVERSITÄT ROSTOCK | LEHRSTUHL FÜR Modellierung und SIMULATION

Spectraldensityofthekineticenergy

E(k) dkisthecontributionofoscillationswiththewavenumbers k<k<k+dk

tothekineticenergyofthe turbulent motion.

E(k) isthedensityofthekineticenergydepending on wavenumbers.

The dependence E(k) isreferredtoastheenergyspectrum

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION