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 around X = 200mm 5.2 Evolution of k and 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. [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] [m/s] [(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. [m2/s2] 4. [m3/s3] 5. [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] [(m/s)**2] [(m/s)**3] [(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 ; ; for p = 1; 2; 3; 4 and q + r < 4. (eg. ) 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 ; ; for p = 1; 2; 3; 4 and q + r < 4. (eg. ). 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 . 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] [(m/s)**2] [(m/s)**2] [(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] [(m/s)**3] [(m/s)**3] [(m/s)**3] [(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] [(m/s)**4] 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] [m/s] [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] [(m/s)**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] [(m/s)**3] [(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] [(m/s)**4] [(m/s)**4] [(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] [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] [(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] [(m/s)**3] [(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] [(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] [m/s] [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 3 *a.ml3 2 3 *a.ml3 2 3 *a.ml3 2 4 *a.ml4 3 3 *b.ml3 3 3 *b.ml3 3 3 *b.ml3 3 3 *b.ml3 3 4 *b.ml4 3 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 . 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.