



                        Description  of  the  data  base:


           Plane  turbulent  mixing  layer  from  C.E.A.T.  Poitiers

                             Joel Delville



                              CEAT/LEA UMR CNRS 6609

                 43, route de l'aerodrome F-86036 Poitiers cedex

                                      - FRANCE -



                           Email:  delville@univ-poitiers.fr



                          June 1995       rev 2 (October 1997)


Contents
1   Brief description of the data base 
    1.1    Quick overview 
    1.2    Flow under study
    1.3    Quantities provided 
    1.4    Structure of the data base 
           1.4.1    Directory data   
           1.4.2    Directory balance 
           1.4.3    Directory turb   
           1.4.4    Directory doc  
           1.4.5    Directory figures  
           1.4.6    Directory pdf 
           1.4.7    Directory spectra 
           1.4.8    Directory ic  
           1.4.9    Directory flow
           1.4.10   Directory PDF2


2   Experimental facility  
    2.1    Wind Tunnel  
    2.2    Generation of the flow 
    2.3    Measurement Configuration 
           2.3.1    Hot-wires and Constant Temperature Anemometry 
           2.3.2    Temperature measurement 
           2.3.3    Data Acquisition  
    2.4    Calibrations 
           2.4.1    Single wire probe 
           2.4.2    "X" wires probe 


3   Flow feature and notations.     
    3.1    Coordinates 
    3.2    Notations  
    3.3    Data reduction
    3.4    Pressure gradient
    3.5    Boundary layers on the plate  


4   Description of experiments   
    4.1    Experiment I : single wire - analogic treatment 
           4.1.1    Measurement grid  
           4.1.2    Files 
           4.1.3    Visualizing the raw data 
           4.1.4    Related data 
           4.1.5    Measurement at the trailing edge of the plate 
    4.2    Experiment II : single wire - sampled data 
           4.2.1    Measurement grid 






           4.2.2    data acquisition configuration 
           4.2.3    Files 
    4.3    Experiment III : "X" wire - sampled data 
           4.3.1    Measurement grid
           4.3.2    data acquisition 
    4.4    Comparison of moments obtained by the different experiments.
           4.4.1    Files 
           4.4.2    Drawing and comparison of measured quantities
    4.5    Spectra
           4.5.1    Files 
           4.5.2    Figures 
    4.6    Probability Density Function  
           4.6.1    Files 
           4.6.2    Figures


5   Energy, Shear-stress and Momentum balance 
    5.1    Files 
    5.2    Energy balance
           5.2.1    Convection
           5.2.2    Diffusion 
           5.2.3    Production
           5.2.4    Dissipation 
           5.2.5    Balance 
    5.3    Shear stress balance
           5.3.1    Files 
           5.3.2    Balance
    5.4    Momentum balance
           5.4.1    Files  
           5.4.2    balance


A   Characteristic quantities for the mixing layer 


List   of   Figures

    2.1    Wind tunnel
    3.1    Coordinates and notations in the mixing layer 
    3.2    Typical mean velocity profile in a plane mixing layer
    3.3    Mean velocity profile at x = 0:5mm from the trailing edge.
           Experiment I
    3.4    RMS velocity profile at x = 0:5mm from the trailing edge.
           Experiment I 
    4.1    Typical mean_velocity profile measured in the mixing layer. 
    4.2    Typical u2  velocity profile in the plane mixing layer. 
    4.3    downstream evolution of the vorticity thickness and momentum thickness
    4.5    Sample of spectrum measured during experiment 2.  For a probe location 
           in the high velocity side of the mixing layer.  X=200mm
    4.6    Sample of spectrum measured during experiment 2.  For a probe location
           in the high velocity side of_the mixing layer.  X=800mm
    4.7    Comparison of U   obtained from the different experiments
    4.8    Comparison of second order moments obtained from the different
           experiments
    4.9    Comparison of third order moments obtained from the different
           experiments
    4.10   Comparison of fourth order moments obtained from the different
           experiments
    4.11   Sample of spectrum of u measured during experiment 3. For a probe 
           near the mixing  layer axis.  X=800mm 
    4.12   Sample of spectrum of v measured during experiment 3. For a probe
           near the mixing layer axis.  X=800mm
    4.13   Sample  of  spectrum  of  w  measured  during  experiment  4.
           For  a  probe  near  the   mixing layer axis.  X=800mm
    4.14   Sample of PDF of u measured during experiment 3.  For a probe near 
           the mixing layer axis.  X=800mm
    4.15   Sample of PDF of v measured during experiment 3.  For a probe near
           the mixing layer axis.  X=800mm
    4.16   Sample of PDF of w measured during experiment 4.  For a probe near
           the mixing layer axis.  X=800mm  
    5.1    Evolution of k and <uv> around X = 200mm 
    5.2    Evolution of k and <uv>  around X = 800mm
    5.3    Evolution of the terms involved in the convective part of the balance
           of k ; X = 800mm  
    5.4    Evolution of the terms involved in the diffusive part of the balance 
           of k ; X = 800mm 
    5.5    Evolution of the terms involved in the productive part of the balance 
           of k ; X = 800mm 
    5.6    Evolution of the dissipation (experiment 2 and balance of k) ;
           X = 800mm 
    5.7    Energy balance at X = 200mm
    5.8    Energy balance at X = 800mm
    5.9    Shear-stress balance at X = 200mm 
    5.10   Shear-stress balance at X = 800mm 
    5.11   Momentum balance at X = 200mm 
    5.12   Momentum balance at X = 800mm 






Chapter   1


Brief   description   of   the   data   base


convention:  In this data base the main directory is noted:  SHL04



1.1       Quick  overview


This  data  base  of  a  plane  turbulent  mixing  layer  contains  two  levels  of
data.  The main features of the flow,  the turbulent quantities and energy
balance  are  contained  in  the  following  directories

    o  SHL04/facility  :  wind  tunnel  and  notations
    o  SHL04/ic  :  initial  longitudinal  velocity  profile
    o  SHL04/turb  :  interesting  turbulent  quantities
    o  SHL04/balance  :  turbulent  energy  balance


More detailed data, including spectra and Probability Density Functions
are  also  available.

    To get a quick overview of what this data base contains, type SHL04/mkovrvw
this  script  file  will  display  on  your  X  terminal  the  main  quantities 
available.




1.2        Flow  under  study

This data base presents results concerning a plane  turbulent  incompressible 
mixing  layer: air-air.  The mixing layer flow is generated from the confluence of
two air streams merging from the  trailing  edge  of  a  thin  flat  plate.   
The  boundary  layers  over  this  plate  are  turbulent.   The velocity ratio is 
of the order of 0.6.  The mean velocity of the high speed stream is noted Ua  and
the corresponding velocity for the low speed part is Ub.




1.3        Quantities  provided


Three experiments are performed by using hot wire anemometry (constant temperature
anemometers). Single wire probes and X wires are used. From this set of experiments
the following quantities are provided.

    o  Mean an MS longitudinal velocity profiles measured at more than 20
       downstream location
    o  High order moments of the velocity fluctuations (up to order 4) measured 
       at 6 downstream        locations
    o  spectra of velocity
    o  Probability density function of velocity
    o  balance of kinetic energy and of the shear stress uv
    o  velocity profile close downstream of the trailing edge



1.4        Structure  of  the  data  base


All the data are saved in ASCII format, in a way compatible with the Gnuplot 
package.


The directories hierarchy is as follows:

           ./data
           ./balance
           ./turb
           ./doc
           ./figures/rawdata
           ./figures/facility
           ./figures/balance
           ./figures/spectra
           ./figures/pdf
           ./pdf
           ./spectra
           ./ic
           ./flow
           ./prog
           ./ps
           ./tex
           ./PDF2

where ./ is the home directory SHL04



1.4.1       Directory  data
Contains the data files.  Generated by the measurements. The units used are metric.



1.4.2       Directory  balance
Contains data files where a few quantities have been calculated, and that are
useful for the momentum balance.  This quantities are properly normalized. 
See section 3.3.



1.4.3       Directory  turb
This directory contains the turbulent quantities properly normalized.  
See section 3.3.



1.4.4       Directory  doc
Contains Files describing the data base.  Three versions are available: LATEX file,
plain ASCII or ps files.



1.4.5       Directory  figures
This directory and the different subdirectories contains Gnuplot scripts   *.gp 
allowing to generate the plots.  Three kinds of scripts are provided

    o  for viewing on a X terminal:  first characters "xt"
    o  generating LATEX files:  first characters "la"
    o  generating Postscript files:  first characters "ps"

    When ran these scripts will fill the subdirectories ps and tex


Subdirectory rawdata
Contains Gnuplot scripts to plot the raw data.


Subdirectory facility
Contains a few figures that describe the flow configuration.


Subdirectory balance
Contains Gnuplot scripts to plot the balance of the turbulent kinetic energy


Subdirectory pdf
Contains Gnuplot scripts to plot the Probability Density Function of u

Subdirectory spectra
Contains Gnuplot scripts to plot the Spectra of u



1.4.6       Directory  pdf
Contains the PDF of u

1.4.7       Directory  spectra
Contains the Spectra of u

1.4.8       Directory  ic
Contains the initial conditions of the flow.  A velocity profile measured
downstream close to the trailing edge of the plate.

1.4.9       Directory  flow
Contains files summarizing the main features of the flow.

1.4.10        Directory  PDF2
Contains PDF of velocity differences.



Chapter   2


Experimental   facility



2.1       Wind  Tunnel


The experiments are performed in the E300 open loop wind tunnel of the C.E.A.T.
Poitiers (see Fig- 2.1 for a description).  It is composed of the following parts,
from upstream to downstream:


o filters to avoid probes contamination
o a converging part (contraction ratio 16) with a square section.
o the test section.  The lower and upper walls can be slanted to adjust pressure 
 gradients
o a diffuser
o an axial fan
o a silencer

                 WIND TUNNEL E300 of the C.E.A.T. Poitiers France


             Type:                         open loop
             Test section:                 square - 300mmx300mm - length :  1.2 m
             Contraction ratio:            16
             Motor and fan:                power :  4.2 kW up to 3,200 rpm
             Rotation of the fan :         can be varied in a ratio of 10
                                           (for probe calibration purposes)
             Temperature:                  regulated  0.5 degrees Celcius
             Probe holder:                 motions along 3 orthogonal axis via 
                                           stepping  motors - accuracy 1/100mm


2.2        Generation  of  the  flow


A duraluminium flat plate separates the converging part of the wind tunnel in two 
symmetrical parts.  Head loss filters are located at the entrance of one of the 
halves.  The characteristics of this plate are:

    o  length:  1m
    o  thickness:  3mm
    o  sand paper is glued on the upstream sides of the plate in order to 
       stabilize the boundary  layers on this plate
    o  downstream edge:  slanted symmetrically with a slope of about 3% - length 
       of the beveled edge 50mm.

The  head  loss  filters  create  a  velocity  difference  between  the  upper  
and  lower  part  of  the  test section entrance.  This velocity difference
creates a plane mixing layer.

The roof and floor of the test section are slanted in order to get a zero pressure
gradient.



2.3        Measurement  Configuration

2.3.1       Hot-wires  and  Constant  Temperature  Anemometry

The experiments are performed by using hot wire anemometry and constant
temperature anemometers.  Two kinds of probe are used

    o  a single probe :  home modified DANTEC 55P11 - wire W-Pt length 0.5 mm ;
        diameter 2.5 micrometers
    o  a 2 wires miniature end flow "X" probe :  standard TSI 1248 - spacing 
       between wires 0.5mm  - wires length 1mm ; diameter 5 micrometers

Anemometers are built from TSI 1750.


2.3.2       Temperature  measurement

Temperatures are measured by using a K-type thermocouple and an Omega cold junction
compensator


2.3.3       Data  Acquisition

Two data acquisition systems are used for the present experiments

    o  The first one is devoted to measurements of Temperature,  mean and RMS 
       voltages.  It is   built from a Keithley 705 10 channels scanner and a
       Keithley 195A digital multimeter. These  devices are controlled via a GPIB
       bus by a PC micro-computer.  This configuration is used  for experiment I 
       only (see 4.1)

    o  The second one is devoted to the data acquisition of instantaneous signals.
       It presents the  following characteristics:

         -signal conditioning by analog separation of mean and fluctuating voltages
         -programmable amplification for gains up to 10240
         -programmable anti-aliasing filters (-36dB/octave)
         -Analog Digital Converters - 12 bits - Voltage range  5V
	 -simultaneous sampling up to 100 kHz
         -aximum continuous record size 512k samples
         -these devices are controlled by a PC micro-computer via a GPIB bus, 
          and a CAMAC  crate controller.


2.4       Calibrations

2.4.1       Single  wire  probe

The calibration law which is used is:
       e**2 (t) = (Tw  - Tf ) x (a + b*u(t)**n )                         (2.1)


       e(t)        is     the instantaneous output voltage from the anemometer
       u(t)        is     the instantaneous streamwise velocity
       Tw          is     the wire constant temperature
       Tf          is     the flow temperature
       a, b, n     are    calibration coefficients

The calibration is performed in the non turbulent high speed side of the wind 
tunnel.  During the calibration the temperature of the mean flow Tf  and the
global velocity Uc of the wind tunnel are varied in an uncoupled way.  This
allows to determine the coefficients a, b, n and the temperature of the wire via 
a regression procedure.



2.4.2       "X"  wires  probe

The calibration law used is for a wire i:


            e**2 / (Tw  - Tf ) = Ca(alpha) + Cb(alpha) * u(t)**n       (2.2)


where
    e             is     the instantaneous output voltage from the anemometer
    Tw            is     the constant temperature of wire 
    u(t)          is     the instantneous velocity normal to wire 
    alpha         is     the instantaneous angle between the velocity vector and
                         the probe axis in the plane defined by the wires.
    n             is     a calibration coefficient chosen independent of alpha
    Ca, Cb        are    calibration coefficients


The calibration is performed is a small jet facility.  During this calibration, 
the mean velocity, the temperature of the flow and the yaw of the probe are varied.
The coefficients Twi , ni and the laws Ca(alpha) and Cb(alpha) are calculated by
a regression procedure.  The calibration is performed for a range of  30 degrees 
for the angle alpha.

   For the experiments involving X-wires (experiments 3, 4, 5), we use non
linearized calibration laws.   In  the  single  wire  experiments  (experiments  1
and  2)  we  use  a  linearized  version  of  the calibration law (equation 2.1)
then the output fluctuating voltage of the anemometer is supposed
to be linearly related to the fluctuating part of the velocity.



Chapter   3


Flow   feature   and   notations.



3.1        Coordinates


The frame of reference is described on figure 3.1.  The coordinates are:
       Ox     streamwise direction starting from the trailing edge of the plate
       Oy     normal to the plate starting from trailing edge
              y > 0 for the high velocity side
       Oz     spanwise direction



3.2        Notations

                      Ua          mean velocity (high speed side)
                      Ub          mean velocity (low speed side)
                      Uc          average convection velocity Uc = (Ua + Ub)=2
                      Delta U     velocity difference:   Delta U = Ua - Ub
                      delta_omega conventional vorticity thickness (see Fig-3.2)
                      X0 ; Y0     virtual origin of the mixing layer (see Fig-4.4)
                      Theta       momentum thickness
                      sigma       expansion factor



3.3        Data  reduction.


When plotting normalized data, the velocity difference  Delta U  and the vorticity
thickness delta_omega  will be used.
                              
3.4       Pressure  gradient

The pressure gradient dp/dx is adjusted as close to zero as possible. This is
performed by achieving a divergence between the roof and the floor of the test
section.



3.5       Boundary  layers  on  the  plate

The use of the sand paper and of a long plate allows both boundary layers to be
fully turbulent at the trailing edge of the plate.  Table 3.1 summarizes the main
features of these boundary layers


Characteristic quantity |  Notation  | High velocity side |   Low velocity side
 measured_at_X=-10mm    |            |   boundary_layer   |   Boundary_layer   
                        |            |                    |                    
Velocity                | Ua, Ub     |   Ua=41.54m/s      |   Ub=22.40m/s      
thickness (99%)         | delta      |   9.6mm            |   6.3mm 
displacement thickness  | delta1     |   1.4mm            |   1.0mm 
momentum thickness      | theta      |   1.0mm            |   0.73mm
shape factor            | H          |   1.35             |   1.37
Reynolds number theta   | Re         |   2900             |   1200
turbulence level        | u'/U       |   ~0.3%            |   ~0.3%

Table 3.1:  Main features of the boundary layers of the separating plate
(measured at the trailing edge).


Some velocity characteristics just downstream the trailing edge can be found in 
Fig-3.3, Fig-3.4, where profiles of mean value and variance of the streamwise 
component of the velocity are plotted respectively.



Chapter   4


Description   of   experiments


The aim of the experiments provided in this data base was to check an experimental
procedure allowing to obtain the balance of turbulent kinetic energy.  The use of 
this procedure on a well documented flow:  the plane mixing layer seemed to be a
reasonable check. To perform this check 3 sets of experiments are used

 o Experiment I : single wire - analogic treatment:  main qualification of the flow
 o Experiment II : single wire - sampled data:  estimation of dissipation
 o Experiment III : "X" wire - sampled data:  estimation of various turbulent 
   quantities, useful  for checking the energy balance.

          -  Experiment III-a or (3)- wires in the xy plane
          -  Experiment III-b or (4)- wires in the xz plane
          -  Experiment III-c or (5)- wires in a 45 degrees plane

During  all  these  experiments,  the  temperature  of  the  flow,  and  a 
reference  velocity  (lower  side velocity) are continuously measured.  The mean
temperature of the flow is kept close to 20o C


4.1       Experiment  I  :  single  wire  -  analogic  treatment


This experiment has been performed in order to characterize the main features of
the flow.  The measurements provide:

    o  The mean velocity
    o  the variance value of the fluctuating velocity

4.1.1       Measurement  grid

The following X locations are investigated (measured from the trailing edge of the
plate): X = 30.0, 40.0, 50.0, 70.0, 100.0, 130.0, 170.0, 200.0, 250.0, 300.0, 
350.0, 400.0, 450.0, 500.0, 550.0, 600.0, 650.0, 725.0, 750.0, 800.0, 850.0, 
900.0, 950.0, 1000.0 mm


    For each X location, 201 measurement locations are used in the Y  direction. 
The extent of the measurement domain is adapted to the mixing layer size.




4.1.2       Files

  The corresponding files are in the directory SHL04/data.

  file names DDDD.ml1, where DDDD is the X  location written using 4 digits and 
leading zeros.  (ie.   0005.ml1).
      A header of 4 lines describes the file contents.  Then the data follow 
organized in 4 columns:


     1.  X location [mm]
     2.  Y  location [mm]
     3.  U  mean velocity [m/s]
     4.  <u**2>    [m2/s2]


      Example of file content:


#  FILE  0030.mls
#SINGLE  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#data  taker:  J.  Delville  CEAT  Poitiers  -  France
#    X   [mm]          Y  [mm]          <U>  [m/s]       <u'u'>  [(m/s)**2]
  0.300000E+02     -0.118200E+02      0.223847E+02      0.478949E-02
  0.300000E+02     -0.116080E+02      0.223880E+02      0.606776E-02



  4.1.3       Visualizing  the  raw  data

  The raw data can be visualized by using the Gnuplot file 
SHL04/figures/rawdata/xtml1.gp


  The script file SHL04/figures/rawdata/makefigs creates


      o  LATEX files (stored in SHL04/tex), names: ml1DDDDm.tex for mean 
velocity and ml1DDDDf.tex  for fluctuating part.  DDDD is the X location written 
using 4 digits and leading zeros.

      o  a single Postscript file (stored in SHL04/ps), named psuml1.ps that 
contains all the plots  directly printable.

      o  Encapsulated  Postscript  files  (stored  in  SHL04/ps),  names  with 
the  same  rules  as  the LATEX ones, but the extension is now   .eps.


Figure  4.1 and  4.2 gives examples of such plots.



      4.1.4       Related  data

      From the mean velocity profiles the following quantities have been computed


          o  downstream evolution of Ua  and Ub
             The corresponding data file is SHL04/flow/uaub.ml1
          o  vorticity thickness (Ua - Ub)=(@U=@y) on the mixing layer axis
             The corresponding data file is SHL04/flow/delom.ml1
          o  momentum thickness. The corresponding data file is
             SHL04/flow/theta.ml1
          o  expansion factor of the mixing layer
          o  iso-velocity lines 
             The corresponding data file is SHL04/flow/thephis.ml1
          o  virtual origin of the mixing layer



      Visualizing related data

      These related data can be plotted by using 
SHL04/figures/rawdata/xtscales.gp.  Figure 4.3  shows the downstream evolution
of the vorticity thickness and momentum thickness.


       The iso-velocities are plotted by using 
SHL04/figures/rawdata/xtthephi.gp.  (Figure 4.4)




4.1.5       Measurement  at  the  trailing  edge  of  the  plate

Experiment  I  has  also  been  performed  close  downstream  the  trailing  edge
(X  ~  0:5mm)  the corresponding data file is SHL04/data/0001.ml1 the 
corresponding plot file is: SHL04/figures/rawdata/xtprofin (cf Fig. 3.3 and 3.4)


4.2       Experiment  II  :  single  wire  -  sampled  data


In this experiment we are mainly interested in the determination some statistics  
concerning the longitudinal component of the velocity:

    o  higher moments
    o  spectra from which an estimation of the dissipation term epsilon can be 
       provided



4.2.1       Measurement  grid

This experiment has been performed at two X  locations :  X=200mm and X=800mm from
the trailing edge.  In the Y  direction, 41 positions are explored.

    o  for X =200mm the measurement step is ffiy= 1.575 mm
    o  for X =800mm the measurement step is ffiy= 2.15 mm



4.2.2       data  acquisition  configuration

At each Y  location, two samples of 512k instantaneous conversions are stored. 
The sampling frequency is 50kHz.  An anti-aliasing filter is used with a cut-off 
frequency fc=20kHz.

4.2.3       Files

Higher moments

The data corresponding to the higher moments can be found in SHL04/data.  
These files are: 0200.ml2  and  0800.ml2.   In  these  files,  are  found  4 
lines  of  header,  followed  by  41  lines  of  6 columns.

   1.  X location [mm]
   2.  Y  position [mm]
   3.  <u**2> [m2/s2]
   4.  <u**3> [m3/s3]
   5.  <u**4> [m4/s4]
   6.  an estimation of the dissipation epsilon obtained from spectra [m2/s3]. 
This dissipation is obtained by assuming isotropy of small dissipative scales and
by using a Taylor hypothesis.  Following these assumptions:

Example of file content:

  FILE  0200.ml2
#SINGLE  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#data  taker:  J.  Delville  CEAT  Poitiers  -  France
# X [mm]   Y [mm]   <u**2>  [(m/s)**2]  <u**3>  [(m/s)**3]  <u**4>  [(m/s)**4]  eps
0.200000E+03 -0.295600E+02  0.766937E-02  0.499922E-03      0.662172E-03  ....


Spectra

The spectra files are in the directory SHL04/spectra.  The generic name is
s0200ml2.DDD for the location X=200mm.  Where DDD is a three digits representation
of the probe location varying  from 001 to 041.
    A header of 4 lines describes the file content. 1024 frequencies are available.
  Then the data follow organized in 3 columns:

   1.  f  frequency [Hz]
   2.  Y  location [mm]
   3.  S(f ) energy at frequency f . 

Example of file contents:

#  File  s0200ml2.016
#SINGLE  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  f   [Hz]      y      [mm]              S(f)
       6.10352     -5.93500      11.2115
       30.5176     -5.93500      11.2115


Data visualization

    o  Spectra plots are generated by using the script file 
       SHL04/figures/spectra/makefigs.   These plots can be viewed by using:  
       gnuplot  xtspml2.gp Figures 4.5 and   4.6 show two typical spectra obtained
       during this experiment.
    o  Higher moments plots can be obtained by using the script-files described in
       section  4.4.2

4.3        Experiment  III  :  "X"  wire  -  sampled  data


This experiment is performed with a X-wires probe.  Three configurations of probe 
orientation are used:

    o  wires in the xy plane:  experiment IIIa_(3) The probe provides u(t); v(t).
       By this way one can measure the turbulent quantities <u** p>;  <v**p>;
       <u**q*v**r>  for p = 1; 2; 3; 4 and q + r < 4.  (eg. <u**3*v> )
    o  wires in the xz plane:  experiment IIIb_(4). The probe provides u(t); w(t).
       By this way one can measure the turbulent quantities <u**p>; <v**p>;  
       <u**q * w**r> for p = 1; 2; 3; 4 and q + r < 4.  (eg. <u**2 w**2> ).
       The moments involving odd powers of w have been checked to be close to 
       zero, as it should be due to the homogeneity in the Z direction.
    o  wires  in  the  xt  plane:  experiment  IIIc  (5).  In  this  configuration,
       the  probe  is  rotated  45 degrees on its axis.  The probe provides 
       u(t); (v(t)-w(t)).  This experiment is performed in  order to get an 
       estimation of the moment <v* w**2>.


4.3.1       Measurement  grid

Experiments  IIIa  (3)  and  and  IIIb  (4)  are  performed  at  6  downstream 
locations:  X=150,  200, 250mm and X=650,800,950mm.  The first three are located
upstream of the self similar region of the flow, while the last are located in the
self similar region.  Experiment IIIc (5) is only performed at locations X=200 and
800mm.

4.3.2       data  acquisition

At each Y  location,  two samples of 512k instantaneous conversions are stored for 
each velocity component.  The sampling frequency is 50kHz.  An anti-aliasing 
filter is used with a cut-off frequency fc=20kHz.

4.4        Comparison  of  moments  obtained  by  the  different  experiments.


4.4.1       Files

Directory   SHL04/data


File names:   DDDDX.mlY where

    o  DDDD is the X location with leading zeros (DDDD=0150, 0200, 0250, 0650, 
       0800 or 0950) 
    o  X corresponds to the order of the moment:
          -   a:  second order moments
          -   b:  third order moments
          -   c:  fourth order moments
          -   m:  first order moment
    o  Y: index of experiment:
          -   Y=3 :  experiment IIIa
          -   Y=4 :  experiment IIIb
          -   Y=5 :  experiment IIIc

Files  description

   Here  are  the  headers  of  the  different  files  involved  in  this  
experiment  for X=200mm


#  FILE  0200a.ml3
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]   Y  [mm]      <u**2>  [(m/s)**2]   <v**2>  [(m/s)**2]  <uv>  [(m/s)**2]
0.200000E+03  -0.295600E+02  0.957454E-02   0.113029E-01     -0.202307E-02

#  FILE  0200b.ml3
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#X[mm] Y[mm] <u**3>[(m/s)**3] <v**3>[(m/s)**3] <u**2v>[(m/s)**3] <uv**2> [(m/s)**3]
0.200000E+03 -0.295600E+02  0.156138E-02 -0.339162E-02 -0.152548E-02  0.158487E-02


#  FILE  0200c.ml3
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#X[mm] Y[mm]  <u**4>[(m/s)**4]     <v**4>      <u**2v**2>      <u**3v>     <uv**3>
0.200000E+03 -0.295600E+02 0.147914E-02 0.265662E-02 0.951231E-03 -0.824148E-03 ...

#  FILE  0200m.ml3
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]   <U>  [m/s]  <V>  [m/s]
    200.      -29.560   22.605499   -0.953397

#  FILE  0200a.ml4
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]          <u**2>  [(m/s)**2]   <w**2>  [(m/s)**2]
 0.200000E+03     -0.295600E+02      0.143306E-01      0.683822E-02

#  FILE  0200b.ml4
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]          <u**3>  [(m/s)**3]   <uw**2>  [(m/s)**3]
 0.200000E+03     -0.295600E+02      0.163858E-02      0.850425E-03

#  FILE  0200c.ml4
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
# X[mm]   Y[mm]    <u**4>  [(m/s)**4]   <w**4>  [(m/s)**4]   <u**2w**2>  [(m/s)**4]
0.200000E+03  -0.295600E+02      0.189589E-02      0.147619E-02      0.694260E-03

#  FILE  0200m.ml4
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]   <U>  [m/s]
    200.      -29.560   22.409800

#  FILE  0200a.ml5
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]          <u**2>  [(m/s)**2]
 0.200000E+03     -0.295600E+02      0.160760E-01


#  FILE  0200b.ml5
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
# X  [mm]  Y  [mm]      <u**3>  [(m/s)**3]          <v**3+  3  v  w**2>  [(m/s)**3]
 0.200000E+03     -0.295600E+02     -0.188325E-02     -0.743583E-04

#  FILE  0200c.ml5
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]          <u**4>  [(m/s)**4]
 0.200000E+03     -0.295600E+02      0.114488E-02

#  FILE  0200m.ml5
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  X  [mm]      Y  [mm]   <U>  [m/s]  <V>  [m/s]
   200.      -29.560   22.538000

4.4.2       Drawing  and  comparison  of  measured  quantities

The data measured via experiments I to III can be compared by using the Gnuplot
script: SHL04/figures/rawdata/xtprof.gp.

    Figures  4.7 to  4.10 shows selected examples of these comparisons for X=800mm

4.5        Spectra


4.5.1       Files


The spectra files are in the directory SHL04/spectra.  The generic name is
s0200mlu.DDD for the location X=200mm, u component ; s0200mlv.DDD and s0200mlw.DDD
for components v and w.  Where DDD is a three digits representation of the probe
location varying from 001 to 041.
    A header of 4 lines describes the file content. 1024 frequencies are available.
Then the data  follow organized in 3 columns:

   1.  f  frequency [Hz]
   2.  Y  location [mm]
   3.  S(f ) energy at frequency f .  The data are normalized by the energy


4.5.2       Figures


The spectra can be plotted by using SHL04/figures/spectra/xtspml*.gp Gnuplot
script files. Examples of spectra are plotted figures 4.11 to  4.13.


4.6        Probability  Density  Function


The PDF are estimated for the 3 components of the velocity.  201 bins are used 
regularly spaced between  5 x the standard deviation.



4.6.1       Files

The  PDF  files  are  in  the  directory  SHL04/pdf.  The  generic  name  is 
p0200mlu.DDD  for  the location X=200mm, u component ; p0200mlv.DDD and
p0200mlw.DDD for components v  and w. Where DDD is a three digits representation
of the probe location varying from 001 to 041.


headers

#  File  p0200mlw.003
#  X  WIRE  MEASUREMENTS  IN  PLANE  MIXING  LAYER
#  data  taker:  J.  Delville  CEAT  Poitiers  -  France
#  w/sigma          y      [mm]             sigma  P(w/sigma)
      -5.00000     -26.5600      1.31225E-02


4.6.2       Figures

The PDF can be plotted by using SHL04/figures/spectra/xtpdf*.gp Gnuplot script 
files.

Examples of spectra are plotted figures 4.14 to  4.16.




Chapter   5


Energy,   Shear-stress   and



Momentum   balance


The flow is supposed to be homogeneous in the Z direction.  The balances are
written:

        ENERGY:  CONVECTION + DIFFUSION + PRODUCTION + DISSIPATION = 0


DISSIPATION =estimated through the spectrum see equation 4.2; or by difference


 SHEAR  STRESS:  CONVECTION + DIFFUSION + PRODUCTION + PRESSURE STRAIN = 0



    These balances are established at two downstream locations : X=200 and X=800mm.

    The first step is to select among the data the ones given the best estimation 
of the turbulent quantity:


                order     turbulent quantity      experiment used          files
                   1         U                       3                     *m.ml3
                   1         V                       3                     *m.ml3
                   2         <uu>                    3                     *a.ml3
                   2         <vv>                    3                     *a.ml3
                   2         <uv>                    3                     *a.ml3
                   2         <ww>                    4                     *a.ml4
                   3         <uuu>                   3                     *b.ml3
                   3         <uuuv>                  3                     *b.ml3
                   3         <uvv>                   3                     *b.ml3
                   3         <vvv>                   3                     *b.ml3
                   3         <uww>                   4                     *b.ml4
                   3         <vww>                   3, 4, 5               *b.ml5
  

    The partial derivatives are performed by a second order finite different 
scheme. Before applying the derivatives, the data are smoothed in the Y  
direction by a FFT procedure:  Fourier transform of size 128 of the profiles 
then rejection of the 20 highest Fourier modes.


5.1        Files

The data corresponding to this part of the study are located in the directory
SHL04/balance.


The selected moments are in the directory SHL04/turb. In this directory can
be also found the data corresponding to the profiles of k and <uv>.  These
profiles are plotted figure 5.1 and 5.2 for the two X locations retained.


All data are stored normalized:


    o  by 1/delta_omega  for the y position
    o  by delta_omega/ = Delta U **3 for the terms of the balance



5.2        Energy  balance


5.2.1       Convection

Figure 5.3 shows for X=800 mm the contribution of the two terms involved in the 
convective part of the balance of energy,  showing the dominant contribution of 
the first term.


Files:  convk.200    and    convk.800



#   File  convk.200
#   Terms  appearing  in  k  convection
#
#          y                u*  dk/dx          v  *dk/dy          convection


5.2.2       Diffusion

Figure 5.4 shows for X=800 mm the contribution of the two terms involved in the diffusive part of the balance of energy, showing the dominant contribution of the 
second term.

Files:  diffk.200    and    diffk.800

#  File  diffk.200
#  Terms  appearing  in  diff  of  k
#
#   y        -.5*d/dx(u3+uv2+uw2)   -.5*d/dy(u2v+v3+vw2)   diffusion


5.2.3       Production

Figure 5.5 shows for X=800 mm the contribution_of the two terms_involved_in the
productive part of the balance of energy, showing the dominant contribution of
the second term.

    Files:  prodk200    and    prodk.800

#  File  prodk.200
#  Terms  appearing  in  production  of  k
#
#   y             -(u2-v2)*dudx          -uv*dudy          production



5.2.4       Dissipation

Figure 5.6 shows for X=800 mm the dissipation ffl estimated from the balance of k 
and the one directly measured by assuming isotropy of the small dissipative scales
and applying Taylor hypothesis (equation 4.2).  The dissipation obtained by the 
second approach is largely underestimated. 

  Files epsl.200    and    epsl.800



#  file  epsl.200
#  dissipation  from  experiment  2
#
#      y              epsilon


5.2.5       Balance

The turbulent kinetic energy balance is plotted on figures 5.7 and 5.8.
Files balancek.200    and    balancek.800


#  File  balancek.200
#  Terms  appearing  in  the  balance  of  k
#           y           remainder        dissipation          dissipation
#                       of  balance     by  difference        from  exp  2


5.3       Shear  stress  balance


5.3.1       Files

Files:  balancuv.200    and    balancuv.800



#  File  balancuv.200
#  Terms  appearing  in  the  balance  of  shear  stress
#
#  y   u*duvdx   v*duvdy   convection     diffusion     production   press`strain



5.3.2       Balance

The shear-stress balance is plotted on figures 5.9 and 5.10.



5.4       Momentum  balance


5.4.1       Files

Files:  momentum.200      and      momentum.800

#  File  momentum.200
#  Terms  appearing  in  the  momentum  equation
#
#  y   u*dudx   v*dudy   -duvdy   -d(u2-v2)dx   u*dudx+v*dudy  -duvdy-d(u2-v2)dx"
   should`be`0   v`from`mom.`bal.



5.4.2       balance

On Figures 5.11 and 5.12, the two terms of the momentum balance are compared.


Bibliography


[1] Delville,  J.,  Bellin,  S.,  Garem,  J.H.  &  Bonnet  J.P. 1988 Analysis of 
structures in a     turbulent a turbulent plane mixing layer by use of a 
pseudo-flow visualization method based     hot-wire anemometry. Advances in
Turbulence II, Fernholz and Fiedler eds., Springer, pp 251.

[2] Delville  J.  1995.  La  decomposition  orthogonale  aux  valeurs  propres 
et  l'analyse  de  l'organisation tridimensionnelle des ecoulements turbulents
cisailles libres. These Doctorat, Universite de Poitiers.






