slide1
Download
Skip this Video
Download Presentation
Basic definitions . Reynolds averaging

Loading in 2 Seconds...

play fullscreen
1 / 11

Basic definitions . Reynolds averaging - PowerPoint PPT Presentation


  • 64 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Basic definitions . Reynolds averaging' - judah


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

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
Basic definitions. Reynolds averaging

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

slide3

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
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

samples1
Samples

Resolution 300 µ

50 mm

2D

Typicaldistributionofthe integral lengthalongthejetmixer.

Scalarturbulence

PLIF Measurementsofthe LTT Rostock

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

typical autocorrelation coefficient along the jet
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

isotropic turbulence
Isotropicturbulence

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

slide8

Isotropic turbulence

Taylor longitudinal length

Taylor transverselength

Taylor Reynolds number

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

correlation function in fourrier space
Correlationfunction in Fourrierspace

Usuallyitispossibletomeasureonlythe

„One dimensional spectralFunction“

UNIVERSITY of ROSTOCK | CHAIR OF MODELLING AND SIMULATION

proof
Proof

UNIVERSITÄT ROSTOCK | LEHRSTUHL FÜR Modellierung und SIMULATION

spectral density of the kinetic energy
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

ad