The construction and development of the multi-component traversing system and associated control hardware and software are presented. A hydrogen bubble/laser sheet flow visualization technique was developed to visually study the characteristics of the mixing layers. With this technique large-scale rollers arising from the Taylor-Gortler instability and its interaction with the primary Kelvin-Helmholtz structures can be studied

Johnston, J. P.

Plesniak, Michael W.

English

NASA Technical Reports Server

Center for flrrbulence Research 
Ann& Research Bn'ef8 - 1988 
N89-22833 
147 
The effects of stabilizing and destabilizing 
longitudinal curvature on the structure 
of turbulent, two-stream mixing layers 
By M. W. PLESNIAK AND J. P. JOHNSTON 
1. Introduction 
1.1 Background 
The topic of the research program is mixing and turbulence transport in par- 
allel, co-flowing, two-stream shear or mixing layers. In particular the effects 
of streamwise (longitudinal) curvature on the growth and development of the 
shear layer were investigated. The preliminary results of the present research 
program are reported in Plesniak and Johnston (1987), where results are pre- 
sented for stable and unstable (in the Taylor-Gortler (T-G) sense) mildly curved 
two-stream mixing layers. These results are compared to a plane mixing layer 
studied in the same facility under nearly identical initial and boundary condi- 
tions. At typical operating conditions, a nominal speed ratio of 0.5 with flow 
speeds of 12 and 24 cm/s was employed. The ratio of the shear layer thickness 
to the radius of curvature is less than 5%. Reynolds numbers based on AU and 
momentum thickness ranged from 1000 to 2000 (5000 to 10000 based on vortic- 
ity thickness) over the region in which measurements were made. Laminar flow 
exists at the splitter plate trailing edge due to the low operating velocities. The 
average momentum thickness Reynolds number in the trailing edge boundary 
layers is estimated to be 190, too low for a trip to be effective. The mixing 
layer was not artificially forced and often exhibited more than one frequency 
of roll up. Dye flow visualization along with single component LDV results are 
presented for all three cases. 
Flow visualization indicated that for stabilizing curvature vortex mergings 
(pairings and triple interactions) are common, but there is little mixing of the 
dye across the layer and fine-scale three-dimensionality does not occur in the 
region studied. Conversely, destabilizing curvature promotes mixing at all scales 
and the layer is characterized by complex three-dimensional structures. Vortex 
interactions are also less prevalent for the unstable case than for the stable or 
plane layers. 
The LDV measurements showed that the unstable layer exhibits a greater 
growth than the plane or the stable layer of nearly the same velocity ratio 
(growth rate was determined from the maximum slope thickness). The mean 
(U) and fluctuating (u') streamwise velocity profiles exhibited self-similarity for 
all three cases studied. However the fluctuating normal (u')  profiles were not 
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148 M. W. PIesniak 8 J. P. Johnston 
self-similar for either the stable or unstable layer. Peak fluctuation levels in both 
components were greatest for the unstable layer. 
1.3 Current Research 
The main goal of the research program is to gain a fundamental understanding 
of the physics of curved, turbulent, unforced free mixing layers and to provide a 
data base for turbulence modelers. Since the facility was previously instrumented 
only with a one-component LDV system, the major objective was to construct a 
two-component LDV system to allow the measurement of Reynolds stresses and 
examine turbulence transport in the mixing layers. 
2. Approach 
2.1 Documentation of Initial Conditions 
It is well known that the scatter in data from various sources regarding free 
shear layers is large. This is due to the mixing layer’s extreme sensitivity to 
initial conditions. A number of studies have been undertaken to examine the 
effects of initial conditions and side-wall confinement effects on the growth of 
free shear layers. These studies attempted to resolve the discrepancies in the 
literature concerning spreading rates and other characteristics of mixing layers. 
However conflicts regarding the effects of laminar vs. turbulent boundary layers 
at separation, initial fluctuation level, initial momentum thickness and influence 
of splitter-plate trailing-edge thickness on the streamwise evolution of the shear 
layer still exist. Some groups report confinement effects of boundaries while 
others do not. 
In view of many unresolved issues concerning initial and boundary condi- 
tion effects it is considered important to document the initial conditions of the 
present study. The two-component LDV system described below is being used 
to investigate the boundary layers on the high and low speed sides of the splitter 
plate. Determination of the momentum thicknesses will allow us to predict the 
most unstable frequency and compare to the results in Ho and Huerre (1984). 
The levels of free stream turbulence in the nozzle will also be measured with 
this system. 
Another issue which has recently been addressed in the literature is spanwise 
nonuniformity in the mixing layer and the formation of small-scale streamwise 
vortical structures due to natural disturbances. Jimenez (1983), Lasheras et a1 
(1986, 1988), Bernal and Roshko (1986), Mehta; Ho (private communications), 
and others have reported on the presence of these structures in plane mixing 
layers. They are easily detectable in spanwise variations of the mean streamwise 
( V )  velocity profiles. Since these structures have never been studied in curved 
mixing layers, it is unknown whether there is any interaction with the T-G 
structures resulting in their suppression or enhancement. 
The eflects of curvature on the structure of mizing layers 149 
2.2 Flow Visualization Studies 
Previous results obtained with vegetable dye visualization were able to show 
diffusion of the dye across the layer and also the entrainment of ambient fluid 
into the layer. VHS format videotape movies showed large-scale structures which 
transported dye across to opposite sides of the shear layer in the case of desta- 
bilizing curvature. However the dye visualization technique had several limita- 
tions: the major being the rapid diffusion of dye in the fully turbulent regimes 
restricting the operating velocities lower than those used in acquiring the quan- 
titative data. 
Thus, for the present study a hydrogen bubble technique with portable laser 
sheet illumination was employed. The wire may be positioned at any location 
in the mixing layer along the entire length of the test section. Using existing 
equipment, timelines can be generated by pulsing the wire. This technique will 
enable us to visualize the transport of turbulence (and of mass if the Schmidt 
number of the bubbles is low enough) by the structures of various scales. In 
particular, the large scale motions associated with the T-G rollers in the unstable 
layer can be studied. A suitable lighting source is currently being sought to 
illuminate a 2-D grid of hydrogen bubble wire used to visualize an entire plane 
across the mixing layer. 
2.3 Velocity Data 
After unexpected delays in delivery of the necessary components the two/three- 
component LDV system has been constructed, optically aligned and calibrated. 
Preliminary two-component velocity profiles have been obtained for the sta- 
ble and unstable layers. However, these data suffer convergence problems in the 
mixed (uu)  moments due to insufficient numbers of samples. More complete data 
being presently acquired correct this problem. In addition the third component 
capability (w measured with an immersible fiber optics probe) has recently been 
added to the system so that the entire 3-D velocity field may simultaneously be 
acquired and the full Reynolds stress tensor computed. 
2.3.1 Description of the 2-Component LDV 
A three-color, two-component LDV system powered by a 3-Watt Argon-ion 
Lexel laser was constructed for turbulence studies in the curved mixing layers. 
The system employs frequency shifting on both channels and is configured to 
operate in the backscatter mode. The entire system is mounted on an opti- 
cal breadboard which may be traversed in a rectilinear X-Y global coordinate 
system. 
An aluminum traversing cart made of 2 x 4 inch square tubing (1/8 inch wall 
thickness) chosen for its light weight and stiffness was constructed to traverse 
the optical system. The traverse rides on pillow block linear bearings over a 1 
inch diameter ground stainless steel shaft. Positioning in the global streamwise 
150 M. W. Plesniak tY J .  P. Johnston 
direction (X) is performed manually over a travel of 12 feet (3.66 m). The 
direction normal to  this (Y) has a travel of 4 feet (1.22 m). Thus, any point 
across the entire outer channel may be accessed. 
In order to traverse along a radial line in the inner curved test section, pro- 
grammable computer controlled stepper motors are used. The stepper motors 
are driven by Superior 430-TH translator modules operating in a chopped mode. 
An Anaheim Automation CL1605 programmable controller board is used to con- 
trol the translator modules. Parameters such as motor speed, acceleration, and 
limit switch condition are controlled by the board. A serial RS-232 interface is 
used to communicate to the CL1605 with the data acquisition computer system. 
A ball nut/screw assembly with a lead of 0.250 in (6.35 mm) is used for 
positioning in the Y direction while a lead screw unislide assembly with a lead 
of 0.100 in (2.54 mm) is employed for fine positioning over 10 inches (0.254 m) 
of travel in the global X direction. The stepper motors are driven in a half- 
step mode which produces a resolution of 400 steps/revolution. This allows a 
positioning resolution of 0.00025 in/step (0.00635 mm/step) in the X direction 
and 0.000625 in/step (0.015875 mm/step) in the Y direction. Backlash in X 
was measured to be 0.001 in (0.0254 mm) and in Y, 0.003 in (0.0762 mm). 
A radial move in the local z-y coordinate system of the curved shear layer 
consists of two moves in the global X-Y coordinate system. The angle between 
a radial line in the local coordinates and the global coordinate system is deter- 
mined experimentally. Considering spatial resolution in X and Y, backlash and 
uncertainty in determining the angle, the resolution in positioning accuracy is 
less than half of the LDV measuring volume diameter (100 microns). 
One limitation of this traversing system is that no automated spanwise travers- 
ing is possible due to design constraints resulting from lack of funding. However, 
the He-Ne based fiber optics probe traverse does have spanwise capability and 
can be used when such measurements are dictated. 
2.3.2 Present LDV Measurements 
The two-component LDV system described above is being used to  make mea- 
surements in the curved mixing layer for three different configurations: straight 
(reference), stable and unstable with a velocity ratio of 2:l. Measurements of 
complete profiles (20 to  30 spatial points) at approximately 8 streamwise sta- 
tions will allow accurate determination of the mean growth rate and evolution 
of the shear layers’ turbulence fields. In conjunction with the fiber optics probe, 
three components of velocity (u, u, w )  can be measured. Acquisition of all three 
velocity components simultaneously allows the entire Reynolds stress tensor to 
be computed and estimates of the turbulent energy budget can be made. Com- 
plete time records are saved at each position for post-processing. Mean and rms 
velocities, Reynolds stresses, higher order moments (skewness and kurtosis), and 
velocity probability density functions will be calculated. 
The eflects of curvature on the structure of mizing layers 151 
Separate runs with much longer record lengths necessary to resolve the lowest 
frequencies will be made for spectral and autocorrelation data acquisition at 
several points in the mixing layer. Since we have two independent LDV systems 
(l-component probe and 2-component system), it will be possible to  obtain two- 
point spatial correlations by positioning the probes at different points in the 
mixing layer. This kind of data may be particularly useful in tracking the large 
T-G rollers in the unstable layers. 
3. Summary 
A major portion of the period covered under CTR funding was spent on 
the construction and development of the multi-component traversing system 
and associated control hardware and software. Delays in delivery of necessary 
components delayed construction by several months. The system was first used 
to make measurements in October, 1988. 
In addition to acquiring the two-component measurement capability, a hydro- 
gen bubble/laser sheet flow visualization technique was developed to visually 
study the characteristics of the mixing layers. With this new technique we can 
look for evidence of the large-scale rollers arising from the Taylor-Gortler insta- 
bility and study its interaction with the primary Kelvin-Helmholtz structures. 
In general, the recently acquired data confirm the results reported in our 
preliminary paper (Plesniak and Johnston, 1987). At  this stage we are making 
two and three-component measurements and will be able to report information 
regarding the transport of turbulence and full Reynolds stress data in several 
months . 
REFERENCES 
BERNAL, L .  P .  AND ROSHKO, A. 1986 Streamwise Vortex Structure in 
Plane Mixing Layers. J. Fluid Mech. 170, 499-525. 
H O ,  C-H AND HUERRE, P. 1984 Perturbed Free Shear Layers. Ann. Rev. 
Fluid Mech. 16, 365-424. 
JIMENEZ J .  1983 A Spanwise Structure in the Shear Layer. J. Fluid Mech. 
132, 319-336. 
LASHERAS, J. C . ,  CHO, J. S .  AND MAXWORTHY, T.  1986 On the Origin 
and Evolution of Streamwise Vortical Structures in a Plane, Free Shear 
Layer. J. Fluid Mech. 172, 231-258. 
LASHERAS, J .  C .  AND CHOI, H .  1988 3-D Instabilities of a Plane Free 
Shear Layer: An Experimental Study of the Formation and Evolution of 
Streamwise Vortices. J. Fluid Mech. 189, 53-86. 
152 M. W .  Plesniak €4 J. P .  Johnston 
PLESNIAK, M. W. AND JOHNSTON, J .  P .  1987 The Effects of Stabilizing 
and Destabilizing Curvature on a Turbulent Mixing Layer, Proc. of the 2nd 
Int'l Symp on Transport Phenomena in Turbulent Flows, Tokyo, October 25- 
29, pub. in ??ansport Phenomena in firbulent Flows: Theory, Experiment, 
and Numerical Simulation, (1988) Hemisphere Publishing Corp., M. Hirata 
and N. Kasagi, ed. 377-390 


The effects of stabilizing and destabilizing longitudinal curvature on the structure of turbulent, two-stream mixing layers

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