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March 1988
AN EXPERIMENTAL STUDY OF A LAMINAR WALL-JET IN THE PRESENCE OF A UNIFORM EXTERNAL FLOW
by
Allan Bradley Paige
EL'
KluyverNeg 1 - 2629 HS DELFT
UTIAS Technical Note No. 268 eN ISSN 0082-5263
AN EXPERIMENTAL STUDY OF A LAMINAR WALL-JET IN THE PRESENCE OF A UNIFORM EXTERNAL FLOW
by
Allan Bradley Paige
Submitted December 1987
© Allan Bradley Paige 1988
t-1a rch 1988
UTIAS Technical Note No. 268 CN ISSN 0082-5263
. Acknowl edgements
The author would like to thank his supervisor, Dr. G. W. Johnston, for his useful recommendations and continuing support throughout this work. Other members of the Aeroacoustics Group at UTIAS, especially Norm Ball, were always available with helpful suggestions and this support is gratefully acknowledged. In addition, this work would not have been possible without the expert machining of the jet nozzle mechanism by Mr. Hans Schumacher.
This work was financially supported by the Natural Sciences and Engineering Research Council of Canada.
.
-Summary
An experimental investigation was earried out with two-dimensional, initially laminar wall-j"ets, both statieally and in a uniform flow, U co. The
" purpose of the research was to quantify transition in the augmented flow
(free streamplus jet), and measure the effects of U and slot height, h, co on transition. As an additional objeetive, a suitable definition for transition of the statie wall-jet was desired.
The experimental statie wall-jet mean velocity profiles were found to be in good agreement with previously developed theories and experiments for both the laminar and turbulent regimes. Jet width, 0, and maximum velocity,
IJ m' varle Wl . d . th 0.75 d -0.50 x an x , respeetlVe y or . 1 f th l ' e amlnar Jet an x . d 1.00
and x- 0•50 for the turbulent jet, where x is the distanee downstream from
the slot. The mean value of the intersection between the differing 0 growth
and Urn deeay lines for laminar and turbulent jets was used to define a
transition point, resulting in the relationship Ro =522.9 + 0.5239Rexit •
trans
Experiments with the augmented flow revealed a delay in jet transition
relative to the statie wall-jet. For h=O.031 inches and Uco~.5 ft/s, the
velocity profiles of the weaker jets (U./U (3.21) nearly return to the
J co
free-stream boundary layer shape af ter dissipation of the jet, while the stronger jets (U
j/U co>3.70) undergo transition in the test seetion but beyond the statie jet transition point. Velocity profiles measured at the end of the test seetion indieate that hand jet exit velocity, U., are the major
J
parameters for determining when an augmented flow will exhibit transition, while U and (U.-U ) are of seeondary importanee.
list of Figures
1. Wind Tunnel Contraction, Honeycomb and Screen Geometry
2. Views of the a) Wind Tunnel and b) Traversing Mechanism With the Probe Assembly Attached
3. Section Through the Jet Nozzle
4. Turbulence Spectrum of the Jet a) Before and b) Af ter ~1odifications
5. Pressure versus Velocity Curve For the Calibration Venturi 6. Typical Calibration Curve For a Hot-Wire Sensor With Non-Linear
Output
7. Two-Dimensionality Check For the 0.067 in. Angled Slot 8. Two-Dimensionality Check For the 0.031 in. Angled Slot
9. Velocity Profiles For a 0.030 in. Parallel Exit Slot With Rexit=639 10. Velocity Profiles For a 0.050 in. Parallel Exit Slot With Rexit=652 11. Velocity Profiles For a 0.031 in. Angled Exit Slot With Rex it=599 12. Velocity Profiles For a 0.067 in. Angled Exit Slot With Rexit=706 13. Time Traces and Frequency Spectra For a) Laminar, b) Transitional
and c) Turbulent Jets
14. Velocity Decay and Jet Growth For a 0.030 in. Parallel Exit Slot With Rexit =628
15. Velocity Decay and Jet Growth For a 0.050 in. Parallel Exit Slot With Rexit=766
16. Velocity Decay and Jet Growth For a 0.031 in. Angled Exit Slot With Rexit=495
17. Virtual Origin Variation With Rexit For Static Laminar Wall-Jets 18. Virtual Origin Variation With Refit For Static Laminar Wall-Jets
With Shifted Rexit'S For the Ang ed Exit Cases
19. Relationship Between Rexit and R"" For a Static Wall-Jet l: rans
20. Velocity Profiles Through Transition For an Acoustically Excited Boundary Layer With U(D=8.45 ftjs
21. Wall Shear and Shape Factor Variation Through Transition For an Acoustically Excited Boundary Layer With U(D=8.45 ftjs
list of Figures (Cont'd)
22. Velocity Profiles For h=0.031 in. and U./U =2.00 J '" 23. Velocity Profiles For h=0.031 in. and Uj /U",=3.00 24. Velocity Profiles For h=0.031 in. and Uj /U",=3.21 25. Velocity Profiles For h=0.031 in. and Uj /U",=3.40 26. Velocity Profiles For h=0.031 in. anc! U/Uco=3.70 27. Velocity Profiles For h=0.031 in. and Uj/U",=3.92 28. Velocity Profiles For h=0.031 in. and U/U",=4.88
29. Typical Time Traces and Turbulent Spectra For an Augmented Flow a) Near The Jet Nozzle and b) Far Downstream
30. Velocity Profiles at X=40 in. For h=0.031 in., U",=8.45 ft/s and Uj /U",=3.12, 3.24, 3.29,3.47,3.66,3.82,4.03 and 4.24
31. Velocity Profiles at X=40 in. For h=0.031 in., UaF12.9 ft/s and Uj /U",=2.09, 2.22, 2.35, 2.50 and 2.65
32. Shape Factor Variation With Rexit at X=40 in. 33. Shape Factor Variation With Uj/U", at X=40 in.
34. Velocity Profiles at X=40 in. for h=0.067 in., U =8.1 ft/s and
'"
U/U",=2.10, 2.25, 2.36, 2.49, 2.60 and 2.74
35. Typical Augmented Flow Velocity Profiles Near The Jet Nozzle For Jets With the Same Rexit But Different Slot Heights
Li st of Symbo 1 s
Hot-Wire Symbols
a hot-wire overheat ratio
E non-linear hot-wire dc voltage at a specific temperature Eo non-linear hot-wire dc voltage at the calibration temperature
R ca+pr Rext R sens T
resistance of cable plus hot-wire leads external bridge resistance
hot-wire resistance specific temperature
room temperature during hot-wire calibration hot-wire temperature 0: êR sens / êT w Flow Symbols h R ex, ·t Ro R Ot rans slot height
critical Reynold's number based jet exit Reynold's number based loca 1 Reynold's number based on Ro at transition
on Um and on U.
J and Um and 0
Ro* local Reynold's number based on Um and ê*
u disturbance velocity, x component u,Uavg mean velocity at a point
U. maximum jet velocity at the jet nozzle J
U maximum velocity in a profile
m
ê h
List of Symbols (Cont1d)
X,x distance downstream from the slot
Y,y distance above the tunnel floor
yu distance above the floor to the point of maximum velocity
m
Z,z distance from the spanwise centreline
a constant in Glauert's turbulent wall-jet theory
v kinematic viscosity
5 wall-jet thickness, the point in the outer half of the jet
where U=O.SUm 5.
99 thickness of free-stream boundary layer
5* di spl acement thi ckness of free-stream boundary 1 ayer
1. Introduction
There are relatively few papers in the literature devoted to the study of laminar wall-jets, either two-dimensional or radial, although turbulent wall-jets have been extensively studied with and without the superposition of a free stream on'the jet. This is probably due to the nature of laminar wall-jet flows which tend to turbulence very soon beyond the nozzle exit. Therefore, in most practical applications such as blowing on a wing surface, a wall-jet will be turbulent.
The first theoretical work on static two-dimensional laminar wall-jets was by Tetervin (1). He determined the characteristics of the flow by numerical integration of the governing equation. His result predicted jet thickness, ó, to be proportional to xO•75 and the local maximum velocity,
IJ , to be proportional to x- O•50• This work was later expanded by Glauert
m
(2,3) who found a closed form similar solution for both the radial and
two-dimensional laminar wall-jet which agreed with Tetervin's work. Chun
and Schwarz (4), using Glauert's similarity velocity profile solved the
Orr-Sommerfeld equation by a Runge-Kutta method to estimate the neutral
stability curve and the corresponding critical Reynold's number, Ró =U ó/v,
cr m
to be 57. Scibilia and Durox (5), employing a modified velocity profile
closely related to Glauert's, solved the Orr-Sommerfeld equation by
Galerkin's method and found Ró =73. Because the Reynold's number based
cr
on U and ó grows as xO.25, this implies th at a laminar wall-jet will
m
eventually go unstable.
The first laminar wall-jet experiments, by Bajura (6) and Bajura and Szewczyk (7), measured velocity profiles for a two-dimensional laminar wall-jet up to 180 slot widths downstream of the exit and found good
ag reement with theory except at the outer edge of the jet. Thei r work showed jet thickness growth and velocity decay to be consistent with Tetervin and Glauert and the virtual origin of the jet linear with exit Reynold's numher, Rexit=Ujh/v. As well, when Rexitwas less than 300,
disturbances were not amplified in the test section while for Rexit greater than 855, transition occured within 180 slot widths of the exit. This
showed that, although Rö is very low, transition will not occur until any
cr
dmplified disturbances become large enough to trip the flow. Bajura and Catalano (8) studied the transition of a two-dimensional wall-jet in water using flow visualization and hot-film probes to measure the turbulence spectrum and interrl'littency. Tsuji et al (9) studied the stabil ity of a two-dimensional wall-jet theoretically and experimentally using an external sound souree to trigger transition. They also neasured velocity profiles from the laminar to turbulent regimes for natural transition. For
Rexit=6A5, transition occurred about 45 slot widths downstream of the exit
1
where Rö was approximately 720.
For statie, turbulent two-dimensional wall-jets, Glauert (2) developed a theory to predict the velocity profile using a varying eddy viscosity, E, in the inner layer and a constant E in the outer layer. He found that
complete similarity is not attainable but depends on a variable a, which varies from 2 for R=10 to 1 for R=~. This variable shifts the location of U
m and slightly alters the shape of the velocity profile. Since then, numerous researchers such as Bakke (10), Gartshore and Hawaleshka (11), George (12), Schwarz and Cosart (13) and Sigalla (14) obtained experimental
profiles that showed reasonable agreement with Glauert. In all cases, ö is
1
In the paper by Tsuji et al, for the graph of (Umh/ v) -2 versus x/h, the scale for (U h/ v)-2 should be to 10-6, not 10- 4•
proportional to x1.00 and Urn is proportional to x-n where O.50<n"Ü.55. These authors all used high Reynold's nurnber jets rnuch beyond transition and
or-1.2 or 1.3 to get the best fit of Glauert's theory to their data. The experirnents in this thesis are at rnuch lower Reynold's numbers and are therefore not directly comparable with the aforementioned works.
Several theoretical and experimental investigations, i.e. Gartshore and NeYnTlan (15), Kruka and Eskinazi (16) and Pat el (17), have been carried out for a turbulent wall-jet in a free stream. These works are valid only for wide and strong jets where there is no velocity deficit (velocity less than
U~) at distances from the wall greater than yU. This is achieved by having
m
a slot height to free-stream boundary layer thickness ratio, h/o.99, of at least one, and taking measurements only in the far field. For the augmented flowexperiments in this work these theories are not applicable in the
turbulent regime because the jets are weak in the far field and h/o.99 is approxirnately 0.05 to 0.20, which leads to very large velocity deficits.
There have been no known previous investigations, theoreticalor experimental, to study the effects of a two-dimensional laminar wall-jet augmenting a free stream. The present experimental work has attempted to quantify the wall boundary layer transition in this type of flow, and especially examined the roles of velocity ratio, U./U , and h/o 99.
J ~ • No
previous experiments have attempted to find an explicit expression for transition in a static two-dimensional wall-jet. Therefore, as an additional objective, such an expression was sought.
2. Wind Tunnel Design
A wind tunnel with a two-dimensional wall-jet insert was designed and constructed for this and future wall-jet experiments. The work of Bajura and Szewcyzk (7) was used as a starting point to estimate the maximum Rexit necessary for the transition experiments, with the result that a maximum Rexit of 750 was used for initial estimates of slot size and velocity. It
was felt that the largest jet possible was desirable at the expense of jet velocity for better definition of the velocity profiles. This led to designing the slot height to be a minimum of 0.020 inches, which gave a maximum jet velocity of 70.8 ft/s for Rexit=750. The experiment was set up to cover velocity ratios (U./U ) from 1.0 to 4.0 for a constant free-stream
J 00
velocity. This meant that the maximum free-stream velocity necessary was 17.7 ft/s to cover all experimental conditions. To accomodate U./U =1.0
J 00
for a free-stream velocity of 17.7 ft/s and Rexit =750, the slot had to be expandable to at least 0.080 inches.
To minimise capital outlays, an available Canadian Blower/Canada Pumps 245 BLVS centrifugal blower with a 1/4 hp electric motor was used to power the wind tunnel. Speed was varied by changing the pulley sizes on the motor and by partial blockage of the fan exhaust port. With the characteristics of the fan known, cross-section area and shape was determined based on two criteria. To achieve two-dimensionality of the jet near the centre-line, a high aspect ratio slot was desired. For this reason, the tunnel was made 15 inches-wide. The low speeds of the experiment meant thick boundary layers 50 the wind tunnel was made 9 inches high to allow the volume flow,
with the fan operating at maximum speed, to maintain a free-stream velocity of 20 ft/s.
For simplicity, the contraction shape was two-dimensional in the Y direction only using the method of Cohen and Ritchie (18). This method, for axisymmetric contraetions, gives a series of diameters along the length of the contraction such that there will be little or no velocity overshoot at the walls and centre-line. These diameters were used as heights for the two-dimensional contraction. Space limitations kept the contraction ratio to 20:9, even though it was realized that a penalty would be paid in
free-stream turbulence levels. To minimize this effect, a 2 inch thick piece of 1/16 inch grid by 0.0007 inch wall thickness honeycomb was placed upstream of the contraction, along with five screens of 54x54 mesh by 0.004 inch diameter wire at 1.5 inch intervals (Figure 1). The resulting
free-stream turbulence levels are less than 0.1% for Um=8.5 ft/se The jet nozzle was placed 12 inches past the end of the contraction with the
test-section extending 42 inches beyond the slot. Provision was made for a suction system to be installed between the end ·of the contraction and the jet nozzle as a means of drawing off the boundary layer but this was not implemented for these experiments. The floor of the test section was made from a piece of 1/2 inch thick clear plexiglass, this being the smoothest material readily available. The walls of the test section diverge 1/2 inch over the 42 inch length for a zero axial pressure gradient. The roof of the test section was made from six 6 inch segments of clear plexiglass, and one 12 inch segment of aluminum onto which the traversing mechanism is mounted. The wind tunnel in Figure 2a was built in an anechoic room first used for jet noise experiments with an exhaust duet for the jets. The duet was modified to fit the diffuser from the tunnel with the centrifugal blower
placed at the downstream end to draw air through the tunnel. Originally, the blower vented outdoors but it was found that for the low veloeities in the experiments, variations in wind speed greatly altered free-stream
velocities in the tunnel. This necessitated blocking the vent and rerouting the air back indoors. To prevent fan noise from migrating upstream and prematurely disturbing the flow, the duct and diffuser were lined with 4 inches of fibreglass insulation and a fibreglass splitter plate was installed.
The wall-jet nozzle was fed by plant air at 80 to 90 psi followed by two pressure regulators which brought the line pressure down to 70 and then 50 psi. Both regulators were necessary to prevent fluctuations in line pressure as the plant pressure dropped to 80 psi and then as the compressor brought the plant pressure back to 90 psi. The air leaving the final
regul ator went through a Whitey Uni on Bonnet S$-3LRF4 preci sion needl e val ve to accurately control the air flow within fine tolerances. A 3/4 inch
flexible plastic line carried the air to the jet plenum below the tunnel where it was expanded to a 15x4 inch cross-section. Following this expansion, the air went through a two-dimensional contraction to a width of from 0.233 inches for a slot height of 0.020 inches to 0.510 inches for a slot height of 0.080 inches. At this point, the flow entered the jet nozzle for contraction to the final slot height and rotation to bring the jet out nearly parallel to the tunnel floor.
The jet nozzle in Figure 3 was flush with the wind tunnel floor, employing an angled exit with the Coanda effect turning the jet until it became parallel to the wind tunnel floor. The reason for choosing this exit configuration was to minimize the jet upper-wall thickness to slot height ratio and this design brought the ratio down to zero at the exit.
If the jet flow entered the free-stream flow parallel to it, there would necessarily be a plate of finite thickness covering the jet before the exit. At the lip of this plate, the thickness would be finite as well causing eddying behind it and premature transition of the jet. A very thin plate
would get around this problem but this is not reco~mended due to the
possiblity of warpage and the resulting uneven slot widths. The entry angle was set at 12.50 to minimize the angle to the tunnel floor, maximize the sharpness of the top piece of the nozzle and allow the parallel flow section of the nozzle to be at least 3 inches long in a minimum depth. As an added benefit, the shallow angle allowed for finer adjustment in slot height through the horizontal sliding action of the ~ovable part of the nozzle.
The nozzle itself was 15 inches wide with a continuously variable slot height of 0 to 0.080 inches giving an overall contraction of the jet from the plenum of at least 50:1. A contraction ratio of this magnitude was necessary due to the highly turbulent nature of the plant air. During this final contraction the flow was rotated through 77.50 to bring it to the exit angle. A parallel section 3.18 inches long followed to allow for a fully developed parabolic profile at the exit. From Schlichting (19), the inlet length for a straight channel is 1 e =0.0267h 2U m I vso using the extremes
designed for, Urn=71 ft/s may be used up to a slot height of 0.056 inches and the maximum slot hei ght of 0.080 inches may be used up to Um=35 ft/s and a fully developed parabolic profile will still exist at the nozzle exit. This covered all the cases to be dealt with in the experiments.
Originally, the jet plenum was empty except for several screens and a thin piece of fibreglass insulation across the expansion to cause a pressure drop and hence spread the flow to fill the plenum. However, during early tests, discrete peaks in the turbulence spectrum that did not vary with jet velocity were noted (Figure 4), causing high values of the turbulence
intensity. These peaks were attributed to acoustic resonances in the
plenum. As a modification, a piece of honeycomb identical to the type used in the wind tunnel was placed just upstream of the contraction, a 2 inch
thick piece of fibreglass board insulation was located across the middle of the plenum, and the walls were lined with thin pieces of fibreglass. These additions smoothed the spectrum (Figure 4), lowered the peaks, and dropped the overall turbulence levels. The pressure drop across the fibreglass also helped to fill the plenum to the edges without dropping the velocity available at the nozzle exit below that necessary for the experiments.
The final component of the wind tunnel was the traversing mechanism (Figure 2b) that was located on the roof of the test-section. The traverse uses two 20 thread/inch precision screw threads at right angles to each other in a frame that could be mounted for either XV or VZ traverses. The alumimum mounting plate was 12 inches long with two slots mil led at right angles permitting protrusion of the hot-wire sensing probe. The first slot, for VZ traverses, went from the tunnel centre-line at Z=O to Z=±4 inches. This was only used to check two-dimensionality of the flow and then was covered up with masking tape to prevent air leakage. The second slot, aligned for XV traverses along the tunnel centre-line, went from X=-3 to X=+6 inches with one plexiglass roof segment upstream. 8y moving the appropriate number of 6 inch wide plexiglass panels, a V traverse could be carried out at any station in the test-section. During these traverses the unused portion of the slot was sealed to prevent air leakage.
Positioning of the hot-wire probe in the X and Z directions was by marks in 1/2 inch increments on the aluminum plate and by counting 0.05 inches per turn of the screw thread for fine measurements. The probe was positioned in the V direction by a Mitutoyo 500-215 LCD digital vernier caliper attached between the fixed frame of the traverse and the probe hol der assembly. This layout allowed the effect of free play in the screw threads to be ignored as no movement was recorded by the caliper unless the probe assembly moved relative to the frame, no matter what happened with the
screw. The vernier caliper was readable and repeatable to iû.OOOS inches with the capability of being zeroed at any point. This last feature allowed the position of the probe relative to the wall to be set at any station irrespective of the previous coordinates used in the Y direction.
3. Heasurement Techniques
Velocity and turbulence quantities were measured using a constant temperature hot-wire anemometry system by DISA. A DISA 55KOl main unit and 55K10 standard bridge with linearizer were connected to a DISA 55P14 single sensor probe in the wind tunnel via a 5 m cable and a 55H21 probe support. The probe support had a protection pin attached so that when the pin hit the wall, the hot-wire was approximately 0.004 inches higher.
The voltage signal from the hot-wire was available in two forms, linear and non-linear. The linearized signal had the advantage of linear
relationships between the dc voltage and average velocity, Uavg' and the ac or RMS disturbance voltage component and perturbation velocity, u. This allowed the turbulence intensity, defined as u/U avg ,to be calculated directly. One disadvantage is that at the low velocities used in the
experiments, even with maximum gain, the signal lacked s~fficient resolution for an accurate determination of velocity. A second problem associated with low velocities is that electrical noise added by the linearizing circuit accounts for an unacceptably high percentage of the output. The non-linear signal had a higher resolution at low velocities and less electrical noise, but required a calibrated curve of velocity versus voltage over the entire velocity range and did not allow for a direct calculation of the turbulence intensity.
For the above reasons, the non-linear signal was used to get mean velocities even though a more elaborate calibration technique for the hot-wire became necessary. This signal was sent to a Keithley 172A
Multimeter with a 1 millivolt resolution. For measurements of turbulence, the linear signal was used. The low voltage output was not a serious
to U
avg Electrical noise was found to have an insignificant effect on the results.
rbst turbulence in these experiments was found at frequencies of less than 2000 Hz for the higher velocities and 1000 Hz for the lower velocities. To prevent extraneous electrical noise and low frequency waviness in the flow from affecting the turbulence output, the disturbance signal was first passed through an Ithaco 4213 Electronic Bandpass Filter and amplifier set for the 10 to 2000 Hz range. The filtered RMS disturbance voltage was then output on a Bruel and Kjaer Type 2417 Random Noise Voltmeter. Additionally, Spectral Oynamics 5D360 and 50375 Oigital Signal Processors were used to view the frequency spectrum and time trace of the disturbance signal from the hot-wire. The time trace was used to qualitatively estimate the
intermittency of the turbulent bursts for determining transition, while the frequency spectrum was used to show the frequency components in the flow.
Calibration of the hot-wire probe was carried out by one of two
methods. For calibrations early in the experimental period, a rotating arm mechanism powered by a falling weight and damped by a water dashpot was
used. The hot-wire probe, with protection pin attached for accurate modelling of the flow near the probe, was set at a fixed radius and the weight released to rotate the probe through a little more than 360 degrees. A bl ack and sil ver stri ped di sc, rotati ng with the arm, and an LED
photo-diode pair were used to measure the arm's rotation. Each stripe covered 10 degrees causing the amount of light reflected back to the diode to vary systemat i ca lly and the voltage output to do the same. The
non-linear output from the hot-wire and the voltage from the photo-diode were sent to aSpectral Dynamics 50375 Digital Signal Processor and the signals held when the arm reached a steady-state velocity. The time taken for the arm to rotate through 10 degrees along with the radius gave the
probe velocity associated with the captured hot-wire output. This method gave good, repeatible results but was time-consuming so an alternate method was used for later calibrations.
A calibration box using plant air, with a settling chamber followed by a 20.9:1 smooth contraction venturi, was available for calibrating hot-wire probes. A Betz manometer to measure the pressure drop across the contraction is normally used but in the velocity range of interest, the pressure drop was too small for accurate results. Therefore, to amplify the signal to the Betz, a 3/4 inch thick piece of fibreglass board insulation was installed upstream of the settling chamber and a manometer ring placed behind that to allow measurements of the pressure drop from the fibreglass to the venturi exit. Then, using a calibrated probe from the rotating arm mechanism, the pressure versus velocity relationship was plotted for future
use on large scale graphs similar to that in Figure 5. The fibreglass
amplified the signalso that velocities as low as 1 ft/s could be accurately measured, and the needle valve for controlling the jet flow was used to allow for precise alterations in flow speed for good calibrations.
The points obtained by either calibration method were fitted to a curve of the form Eo 2=A + BUc avg (Figure 6) by the method of least squares, with c near 0.5 giving the best results. This curve was valid only at the calibration temperature, To• However, using the method of Kanevce and Oka (20) for data run temperatures, T, within 150 C of To' a correction of the form E~=E2(Tw-To)/(Tw-T) was applied to the voltage. The hot-wire temperature, Tw' was found from resistance measurements of various
components and a, the resistanee change for the wire per degree Celsius, was found from the equations a=a(Tw-T) and Rext=20(Rca+Rsens(1+a)). Rea' Rsens and a are fixed for a given probe but R t' the resistanee of the external ex
bridge, is variable and must be chosen appropriately. T
w must be less than 3000 C to prevent wire oxidation from causing irreversible resistance
changes over a short period of time. Increasing Tw raises the overheat ratio, a, which effectively increases the sensitivity of the probe. As a compromise, Rext was set sothat the zero flow voltage was near 3 volts as recommended by DISA. This gave a wire temperature near 2100 C at room
te~perature and an overheat ratio near 0.7 while retaining good probe sensitivity.
For each calibrated probe, the exact height above the protection pin base had to be determined. The following procedure was used. First, the vernier caliper was zeroed with the pin touching the wall. Next, a piece of 0.020 inch piano wire was placed on the tunnel floor and an open circuit set up with one half attached to the probe leads, the other half attached to the piano wire and both halves going to an ohmmeter. Finally, the hot-wire was lowered onto the piano wire until the resistance first dropped, indicating a closed circuit. The vernier caliper reading was noted and this subtracted from 0.020 inches was the hot-wire height above the tunnel floor with the protection pin lowered onto the floor. This was then used as an offset for all subsequent vernier caliper readings following zeroing of the caliper.
Hot-wire probes are inaccurate at low speeds near solid surfaces due to heat transfer from the probe to the surface. This excess heat transfer causes higher than normal voltages, and hence velocities, to be output. Numerous papers, such as Bhatia et al (21), have been written dealing with empirical corrections that may he made to the output but none were deemed satisfactory. Therefore, no corrections were made but near-wall velocities that were obviously influenced by the wall were ignored in the analysis.
As a check on the two-dimensionality of the angled jet nozzle and to ensure a constant slot width for each case, average velocity profiles were
taken 0.25 inches downstream from the slot at the centre-line and 4 inches off to each side. As examples, the profiles for a 0.067 inch slot with an exit velocity of 18.9 ft/s and a 0.031 inch wide slot with an exit velocity of 28.7 ft/s are shown in Figures 7 and R, respectively. Using the centre-line profile as a baseline, the right and left side profiles can be seen to be close in both shape and magnitude for both cases. However, profiles are sensitive to slot width and this feature was used to minimize slot variations along the span by checking velocity profiles at several spanwise locations and adjusting the slot width as necessary.
For all data runs taken during the experiments, the following steps were taken to make certain that conditions were in equilibrium. All
electrical equipment was turned on at least 15 minutes prior to the start of data acquisition to allow operating temperatures to be reached and
stabilized. The wind tunnel fan was turned on during this time to eliminate any temperature gradients.
While data were being collected, the ambient temperature was noted at regular intervals to allow for updated hot-wire calibration corrections. At each station, before starting to take data, the hot-wire probe/protection pin assembly was brought down to the wall and the vernier caliper zeroed. Data points were always collected from the wall out through the jet or boundary layer and downstream positions were always set by moving toward the desired station from the upstream direction to eliminate the effects of free-play in the screw threads and any hysteresis in the vernier calipers. Voltage outputs, both ac and dc components, were time-averaged for each datum point, the averaging period depending on the amount of fluctuation in the signal.
4. Statie Wall-Jet Experiments
Data were collected for two types of jet nozzles, one with an exit parallel to the floor and the other with a 12.50 angle exit flush with' the tunnel floor. The parallel exit was used to check equipment functionality and experimental techniques, accuracy and limitations by comparison with previous theoretical and experimental work. This exit was made by milling a groove in a piece of 2x2 inch angle aluminum. The groove then had a smooth arc filled in so that when placed over the angle slot, the flow would be smoothly turned through 12.50 and expelled parallel to the wall af ter a short run to develop a parabolic profile. The angle slot was opened to 0.080 inches for these runs so that in the parallel cases, the jet underwent a small contraction through the turn to bring it down to the nozzle heights. The angle exit cases were run to verify that the jet followed the curved approach to the wall without separation using the Coanda effect, and thus gave results similar to those obtained with the parallel exit.
The characteristic velocity at the jet exit was the maximum velocity measured as close to the exit plane as possible. For the parallel nozzle, this velocity was determined by traversing the hot-wire probe upwards across the slot, approximately 0.010 inches downstream, and using the maximum
velocity found. For the angle nozzle a traverse, approximately 0.004 inches above the plate depending on the particular probe, was made in a downstream direction across the slot to find the maximum velocity. It was realized that the velocities found were not the maximum exit velocities but slightly lower peaks at a specific distance past the slot since the probe could not be brought to the exit plane below the tunnel floor for the angle exit. Typical turbulence levels at the nozzle for both types of exits were 0.05 to
0.10% at yU • m
For the parallel nozzle experiments two slot heights, 0.030 and 0.050
inches, were used while for the angle nozzle 0.031 and 0.067 inch slots were
used. For each data run, either full mean velocity and turbulence profiles
or U and 0 only were measured at centreline stations starting just m
downstream of the nozzle and continuing until the jet either became too slow for accurate velocity measurement, or went turbulent. Data were taken into the turbulent regime for comparison with Glauert's (2) turbulent theory and to allow a transition point to be defined.
Velocity profiles for two parallel exit cases and two angle exit cases are presented in Figures 9 to 12, along with the theoretical laminar and turbulent profiles by Glauert. Typical laminar, transitional and turbulent time traces and frequency spectra for the disturbance velocity are shown in Figure 13. The overall data fit is good for both the laminar and turbulent jets. However, the theoretical laminar profile overestimates the velocities for y/o greater than one, as with the results of Bajura and Szewczyk (7) and Tsuji et al (9). With the two parallel exit results, the first station shows an undeveloped profile but this is to be expected since Glauert's solution is for the far field only. However, by the second station, 15 or 25 slot widths downstream, the classic Glauert profile has appeared. The developing profile does not show up as clearly in the angle exit cases because the flow cannot be accurately measured along the curved wall past the exit plane while the profile develops.
As the jet begins to go turbulent, the profile deviates from the
laminar case as different growth and velocity decay laws start to affect the jet. By the time the flow is turbulent, the velocity profile approximates the theoretical turbulent profile. The best fit of Glauert's turbulent
profile to the data came from using ~1.4 in his formulation, which is near that expected for the experimental turbulent RölS of between 700 and 1500. The turbulent profiles compare favourably with that obtained by Tsuji et al, who used a similar velocity range. As Rö increases beyond that of this experiment, the best fit should come from lower alS, as predicted by
Gl auert. This was shown subsequently by Patel (a=1.2, R {42700-83400) and Bakke (a=1.3, Rö~1300) which implies that Glauertls turbulent profiles may be used over a wide range of velocities from the low velocities of this experiment to the high velocities of Patel.
It is desirable to get a good, repeatible definition for the transition point bearing in mind that transition occurs over a region and is not just a single point. This was done in the following manner. Glauert showed that ö«x O•75 and
u
m«x- O•50 in the laminar region and experiments have shown that1.00 -n ( )-2
ö«x and U «x where 0.50<:n<:0.55, in the turbulent region. U hIv
m m
versus x/h has been plotted in Figures 14 to 16 for both angle and parallel exit cases. These graphs show that although U decay is proportional to the
m
-0.50 power for both laminar and turbulent jets, there is a different proport i ona 1 ity constant for the two flow regimes. ( ö/h) 4/3 and ö/h have also been plotted versus x/h in Figures 14 to 16 for the same cases. These graphs distinctly show the different growth rates between the two flow regimes and the straight line fits to the data of (ö/h)4/3 in the laminar region of the flow and ö/h in the turbulent region. As would be expected,
Urn in the turbulent regime decays much faster with x due to greater mixing and for the same reason, ö increases at a faster rate. In the maximum velocity decay graphs, transition is defined as the intersection between the fitted laminar and turbulent U decay lines. In the thickness growth m graphs, the fitted ö/h line in the turbulent region is first raised to the
4/3 power to scale it the same as the fitted (6/h)4/3 line in the laminar region. Then, transition is defined as the intersection between these two lines. As can be seen in Figures 14 to 16, both graph types give nearly
identical estimates for the transition x/ho These are simple and repeatible
definitions for the transition point, and are reasonable because at this point, the flow has deviated from laminar but has not yet established the fully turbulent properties. The average transition x/h from the two methods will be used in later analyses.
Extending the laminar growth or velocity decay lines to the abscissa gave the virtual origin for each jet. The virtual origin has been plotted in Figure 17 using the average results from thickness and velocity plots for
the range of exit Reynoldls numbers used. This plot shows the movement of
the virtual origin with exit Reynoldls number, along with the fitted lines of Bajura and Szewczyk (7) and Reddy Gorla and Jeng (22). The results are in reasonable agreement with the two lines except for a slightly lower slope for each slot height and a lot of scatter between the cases. This is due to inaccurate positioning of the probe relative to the slot. The angle nozzle used an arbitrary origin at the end of the curved entry section, not at the exit plane. The distance along the curved wall from the exit plane to the origin is 0.181 inches or 5.83 slot widths for the 0.031 inch slot, and 0.343 inches or 5.12 slot widths for the 0.067 inch slot so each angle nozzle datum point in the graph was lowered by this amount. Because Rexit for the angle nozzle cases was measured using the maximum velocity at the level of the wal 1 , not at the exit plane, the velocities and hence the RexitlS are too low. This cannot be accurately corrected because x/h for the Urn used is unknown and the velocities cannot be extrapolated back. An estimate of the error was made by extrapolating the known velocity decay
curves back arbitrarily by 5 slot widths from the origin to get a reasonable approximation to the exit velocity. These curves, plotted in Figure 18, show a better fit to the parallel exit data and the fitted lines.
Rö at each station increases proportional to xO.25 and xO.50 in the laminar and turbulent regions, respectively, using the two jet growth and
velocity decay laws. R was estimated for all cases, both angle and
Ötrans
parallel nozzles, using interpolated values for Urn and ö at the ave rage of the transition points defined by the Urn decay and ö growth curves. The
results, plotted in Figure 19, show the variation in Rö with Rexit·
trans
There is a fair amount of scatter in the data but a linear least-squares fit
gives Rö =522.9+0.5239Rexit with a standard deviation of 47.9. R IS
trans ö
were noted for several other runs, not taken through transition due to low
velocities. One case, with Rexit=319, reached Rö=570 at the final station
and was just beginning to depart from the laminar growth line. Using the
fitted line, the expected R for this case is 690±96 at a 75%
Ötrans
confidence level (2 standard deviations). By extrapolation of ö and Urn'
transition was expected by Rö=650 indicating that the fitted line should be a reasonable approximation at low R "tiS as well. ex, From the results of Tsuji et al (9), using the previously defined method for locating the
transition point, R~ =722 for R "t=685. This is lower than the
Utrans ex,
expected Rö =882 but not significantly so, considering the scatter in
trans
the data and the slightly higher initial turbulence levels of 0.2% at Urn
near the exit for their jet. Bajura and Szewczyk (7) did not explicitly
find transition in their experiment but estimated R to be between 500
Ötrans and 2000.
5. Forced Boundary layer Transition Experiment
Before any data could be analyzed for the augmented flow experiments, a definition for transition in this type of flow had to be found. Local turbulence intensity measurements were found to have poor resolution and could not be used to determine transition accurately, so this method was discarded. A second choice was the use of an intermittency function. This is a desirable technique because transition may be defined arbitrarily as
the point downstream where the intermittency is 50%. However, intermittency
could not be measured by this method because the flow did not have the sharp bursts of turbulence necessary for accurate operation of the available
intermittency circuit. This circuit, based on a paper by Hedley and Keffer (23), was designed for a higher velocity range and sharp, distinct turbulent bursts which did not appear in the experimental cases. Alterations to the circuit to lower the usable velocity range did not improve the results so this was also unfortunately abandoned.
Therefore, intermittency and transition points in the augmented boundary layer flow were estimated by two methods. First, careful
observations of the hot-wire disturbance signal's time trace were made to get a qualitative estimate of the intermittency. Second, by measurements of the velocity profiles, shape factors could be estimated. The shape factor, the ratio of displacement thickness, ö*, to momentum thickness,
e,
is a good measure of turbulence in a boundary layer because of the constant butdifferent values of shape factor for laminar and turbulent boundary layers in a zero axial pressure gradient. This means that transition may be defined as a specific intermediate value of shape factor. However, shape factors, as defined for boundary layers, will only give useful results for comparison with unaugmented boundary layer values when no velocity in the
boundary layer exceeds U. Therefore, shape factors are only employed in (X) this experiment far downstream where the jet has dissipated and the flow again resembles a typical boundary layer. All Ö*IS and els were calculated by numerical integration of the data by the trapezoidal rule.
Two data runs were carried out to quantify shape factors and correlate these shape factors with intermittency results from a separate experiment using a flat plate. 1 These runs had a free-stream velocity of 8.6 ft/s, resulting in a boundary layer profile with a displacement thickness, ö*, of 0.09 inches at the beginning ~f the test section and 0.13 inches at the end of the test section, giving an Rö*of 410 and 593, respectively.
Although the free-stream boundary layer profiles were more full than a Blasius profile, the frequencies for amplificaton of Tollmien/Schlichting waves were initially estimated from the neutral stability curve of Saric and Nayfeh (24) for a Blasius profile on a flat plate at zero incidence. The lower limit on frequency was estimated to be 10.6 Hz, this being the frequency at which disturbances would just start to grow for Rö*=593. As an upper estimate, 19.3 Hz was chosen as this is the frequency at which disturbances begin to be amplified at Rö*=433 and stop at Rö*=593. Higher frequencies should cause some amplification, but less than that at 19.3 Hz, so the lower frequency was chosen. Using this range of frequencies as a starting point, a low frequency speaker was selected as a noise source, a cover placed over it and a hose connected to send a sinusoidal disturbance velocity out the jet nozzle. When the experiment was run, frequencies between 11.0 and 16.0 Hz were found to cause transition within the test section, so an intermediate value of 13.5 Hz was used.
For these data runs, velocity profiles were measured and qualitative estimates of the intermittency in the boundary layer made by careful
l Data supplied by UTIAS Ph.D. student N. G. Ball. 21
observation of the time trace. The resulting velocity profiles for one case are plotted in Figure 20 while the shape factors and intermittency estimates for this experiment and the flat plate data run are tabulated bel ow.
Forced Transition Experiment Flat Plate Data Run
X ( in) Shape Factor Intermittency X (cm) Shape Factor Intermi ttency
14 2.20 0 18 2.22 0 20 2.40 0 20 2.07 0 25 2.37 7 22 2.03 10-20 30 2.16 26 24 2.10 20-~0 35 1. 74 48 20 2.03 25-40 40 1.43 81 28 1.89 40-50 45 1.31 91 30 1.81 40-60 50 1.27 94 34 1.56 80-90 60 1.28 97 40 1.47 100 70 1.26 99
Before transition, the shape factor was nearly constant and af ter transition, it began to tend towards a new constant as seen in Figure 22. The experimental wall shear, óU/ LWwall' in Figure 21 was nearly constant before the onset of turbulence but then went through a rapid rise before beginning to level off in the turbulent region. A comparison between the shape factor and wall shear of Figure 21 shows that either could be used to define transition because of the sharp changes in both through transition. However, shape factors were deemed to be more accurate because the errors in velocity near the wall due to hot-wire wall effect have a greater impact on wall shear measurements than on shape factor calculations. The shape factors and intermittency measurements in the previous table show good
used in this case. Using 50% intermittency as the definition for transition, the transitional shape factor is estimated to be 1.74.
A Blasius profile has a shape factor of 2.592 while the laminar
boundary layer profiles in the augmented flowexperiments had average shape factors at X=O and X=40 inches of 2.09 and 2.05, respectively, resulting from a fuller velocity profile. The turbulent profiles in the experiments had a mean shape factor of 1.50 while a 1/7 power law profile has a shape factor of 1.286. The Blasius and 1/7 power law cases are considered to be limits for flows with a zero pressure gradient, with the flat plate data run coming close to these .results, as expected. With the experimental results in between, the transitional shape factor defined above was thought to be reasonable and was used for all the augmented flow experiments.
The free-stream boundary layer profiles in the experiments were fuller than that of a Blasius profile at all stations, resulting in lower shape factors. Initially, it was thought that a favourable axial pressure gradient in the test section might be the cause, but velocity traverses found a zero pressure gradient. The possibility that there was a"memory effect" from the contraction was then investigated using the method of Thwaites (25). This method results in an estimate of shape factor and e,
but predicts no memory effect and a Blasius shape factor. However, this paper also reports that for certain flows the calculated
e
may be more accurate than shape factor. With this in mind, e was calculated by the method of Thwaites, for U =8.5 ft/s in the test section. Starting with ~ 0=0.0 inches at the beginning of the contraction, the calculated e grew to 0.047 inches at the jet slot location. The average experimental value fore
at the slot was 0.0424 inches and this was deemed close enough to account for the deviation from a Blasius shape factor.6. Augmented Flow Experiments
Using the angle jet nozzle, two experiments were run for the initially laminar wall-jet with a free stream superimposed on it, defined as an
augmented flow. In the first experiment, the jet velocity was varied for a
fixed slot height of 0.031 inches and a nominal free-stream velocity of 8.4 ftjs. Mean velocity profiles and qualitative turbulence intermittency estimates were collected along the spanwise centreline, at positions 0.25, 3.0, 12.0, 21.0, 30.0 and 40.0 inches downstream from the jet exit, in order
to determine the flow characteristics. Also, Urn and ö were measured through
transition for the jet alone, for reconstruction of Glauert's laminar profile and estimation of the effect of U on transition in the wall-jet.
CD
Nominal velocity ratios, U.jU , used were 2.0, 3.0, 3.2, 3.4, 3.7, 3.9 and
J CD
4.9 to cover the entire range of events, from the flow remaining laminar throughout to the flow going turbulent in the test section. Measurements were also made of the free stream alone, i.e. U.jU =0.0, for comparison.
J CD
6.1 Velocity Ratios, U./U =2.00, 3.00 and 3.21 J
CD
For these three cases, the flow was laminar at each station in the test section. The mean velocity profiles for each case are plotted with the corresponding free-stream boundary layers and theoretical laminar
wall-jet profiles, in Figures 22 to 24. Immediately downstream of the slot,
the wall-jet dominated the region near the wall, and the augmented flow
profile was nearly identical to the maximum velocity envelope of the
\-/all-jet and the free stream boundary layer. By the end of the test section there was no distinct jet, only a fuller boundary layer. The three cases were nearly identical, except that the jet dissipated more quickly and the
- - ~---
---augmented velocity profile approached more closely the free stream shape at the end of the test section as UjjU~ decreased.
For U.jU =3.21 and 3.00, the corresponding statie wall-jet (the same
J ~
wall-jet configuration with Uj unchanged but no external flow, U~ =0 ftjs) underwent transition near X=6.5 and 7.5 inches, respectively. For the case of U.jU =2.00, the corresponding statie wall-jet remained laminar when the
J ~
downstream veloeities became too low for accurate measurements. A turbulent jet thickens fa ster than a laminar jet, so in the region where the jet still influences the boundary layer with a large peak and the corresponding statie wall-jet is turbulent, the augmented flow peak velocity should be further from the wall than for the laminar jet. This did not occur for these three data runs, as is clearly illustrated in Figure 24 for the case of U.jU =3.21.
J ~ At X=12 inches, yu was similar for augmented and statie jet
m
flows, suggesting the presence of a laminar jet, while the corresponding statie wall-jet went through transition 5.5 inches upstream. This shows that the free stream' is suppressing the turbulence in the jet, so that it remains laminar longer.
Shape factors were measured for the three cases. There was no peak in the augmented boundary layer greater than U by X=12 inches for U.jU =2.00
~ J (X)
and X=21 inches for the two other cases and no visible peak at all at the following station. The measured shape factors for the three cases are listed bel ow. The rise in shape factor with downstream position for
U/U~: 2.00 3.00 3.21 X (i n} Sha~e Factors 12 1.81 .21 1.95 1.91 2.00 30 1.98 1.95 1.99 40 2.01 1.97 1.98 25
U.jU =2.00 and 3.00 was due to further dissipation of the jet af ter the peak
J 00
became less than U. By the final station, the augmented and free stream m profiles were nearly identical for U./U =2.00 where the free-stream-only
J 00
shape factor was 2.02. For Uj /Um=3.00, the shape factor never quite reached
the free-stream-only value of 2.03 at the end of the test section, and it is not known if this would happen further downstream or if the profile would remain more full leading to an early transition in the flow. The case of Uj /Uoo=3.21 did not reach its free stream shape factor of 2.04, and would not
because the decreasing shape factor indicates that the boundary layer is filling out. All the measured shape factors were well above the defined transitional shape factor of 1.74, but most were below the free stream
results because of the increased fullness in the profiles from the additional momentum supplied by the jet.
6.2 Velocity Ratio, Uj/U~3.40
This case, plotted in Figure 25 along with the boundary layer and theoretical laminar wall-jet profiles, was going through transition in the second half of the test section. As before, the jet initially dominated the inner region of the boundary layer, with a fuller profile than for the lower velocity ratios resulting af ter the jet had dissipated. The corresponding statie wall-jet exhibited transition near X=4 inches, while the augmented flow had no turbulent bursting at X=3 inches. Although the corresponding statie wall-jet was not measured in the fully turbulent regime, another
wall-jet similar in velocity and slot height was measured. Extrapolating
these turbulent characteristics to X=12 inches gave Um=2.5 ft/s and yu =0.5 m inches compared to Um=7.4 ft/s and yu =0.14 inches for the extrapolated
laminar jet. It can be seen that the peak present in the augmented flow is nearer to yu for the laminar jet. The peak velocity must also be
m
attributed to a laminar jet flow because the corresponding wall-jet is turbulent by this point and has largely dissipated. This is further proof that the free stream suppresses turbulence in the jet and delays mixing.
Turbulent bursting had begun by X=12 inches and evidence of the increased turbulence may be seen by comparing the augmented profiles with the profiles from· U./U =3.21. At X=12 and 21 inches, the theoretical
J =
laminar wall-jet was thinner with higher peak veloeities for Uj /U==3.40 than for U./U =3.21. Despite this, the peak in the augmented flow was lower in
J =
velocity, occurred further away from the wall, and was broader in width. This indicates increased mixing in the flow and hence greater turbulence for U./U =3.40, as supported by qualitative estimates of intermittency made
J
=
during the data run. The velocity peak was nonexistent by X=21 inches for this case with shape factors at X=21, 30 and 40 inches of 2.09, 1.99 and 1.81, respectively. This decrease in shape factor was due to a fuller
boundary layer and the onset of transition. Although the transitional shape factor of 1.74 was not reached, the flow was very close to going turbulent.
6.3 Yelocity Ratios, U./U =3.70, 3.92 and 4.88
J e
These three data runs became fully turbulent in the test section. The mean velocity profiles, free-stream boundary layer and theoretical laminar wall-jet profiles are plotted in Figures 26 to 28. The corresponding statie wall-jet became turbulent within 2.5 inches for U./U =3.70, and sooner
J
=
for the higher velocity ratios. For Uj /U==4.88, the theoretical laminar wall-jet profiles in Figure 28 are approximate only, due to the very rapid
onset of turbulence. At X=3.0 inches, the near-wall velocity profiles are still similar to the theoretical laminar wall-jet profiles in both magnitude and thickness for U./U =3.70 and 3.92 while for U./U =4.88, thethickness
J ~ J ~
is similar but the sharp statie laminar wall-jet peak has been dissipated somewhat by increased turbulence. Corresponding statie wall-jet results, taken far enough downstream to determine the turbulent jet characteristics, were used to extrapolate the theoretical turbulent wall-jet profiles to X=12 inches. For Uj /U(X)=3.70, the theoretical jet profile has Um=2.64 ft/s at YU =0.56 inches while for Uj /U(X)=4.88, the theoretical wall-jet profile has
m
Um=3.96 ft/s at YU =0.88 inches.
m
For U·/U =3.92, U and yu are in between J (X) m
m
these extremes. Comparing these values with the laminar wall-jet curves and the augmented flow points shows that the peaks are closer to the values of the statie laminar jets than the statie turbulent jets, as these jets have almost dissipated by X=12 inches. This indicates that the flows still exhibit laminar properties, with the free stream suppressing the turbulent mixing and delaying transition beyond that of the statie wall-jet.
At the stations where the jet dominated near the wall, the turbulence was of a high-frequency nature similar to the jet alone. At stations further downstream, the augmented flow had become fully turbulent for all three cases and the turbulence was less spiky with lower frequencies dominating. Sample time traces and frequency spectra for the two types of turbulence are presented in Figure 29.
As the velocity ratio increased, at any given station the laminar wall-jet got thinner with a larger Um. However, as in the comparison between U./U =3.21 and 3.40, the peaks in the augmented flow were broader,
J (X)
occurred further from the wall, and had no appreciable increase in U at the
m
turbulent flow. Because of the large amount of momentum in these jets, the effects were fe1t far downstream, with peaks still slight1y greater than Urn but at large distances from the wa11. By the end of the test section, the velocity profiles were not on1y more fu11, but had a1so taken on typica1 turbulent shapes. That is, oU/oy was 1arger near the wa11, resu1ting in higher near-wa11 ve10cities than for the 1aminar case, but af ter the initia1
rapid rise in velocity, oU/oy decreased below that for a 1aminar boundary 1ayer, resu1ting in 10wer ve10cities and a thicker boundary 1ayer.
From qua1itative estimates of intermittency, the flow was turbulent by X=12 inches with 1itt1e overshoot in velocity from the jet, but it took until X=40 inches for a normal turbulent boundary layer velocity profile to develop due to the amount of momentum from the jet that must be dissipated. Whenever there was any overshoot, the shape factor as defined was not
emp10yed. For Uj/U~=3.70 and 3.92 only the X=40 inch station had no overshoot, with resulting shape factors of 1.61 and 1.64 respectively. This was well below the estimated transitional shape factor of 1.74 and confirmed that the flow was turbulent. For Uj /Um=4.88, the velocity
overshoot never completely disappeared in the test section so no shape factors were calculated.
6.4 Far Field Data Runs
Additional data runs were carried out near the end of the test section at X=40 inches with different hand U combinations to determine the effect
~
of the wall-jet on transition in the augmented flow fol10wing dissipation of the jet. For use as a baseline in this series of comparisons, one further set of data was co11ected for a 0.031 inch slot and a U of 8.45 ft/se This m case used velocity ratios of 0.00, 3.12, 3.24, 3.29, 3.47, 3.66, 3.82,4.03,
and 4.24 measured at X=40 inches. The resultant velocity profiles are plotted in Figure 30. The range of velocity ratios chosen covered the region from fully laminar everywhere to fully turbulent at the end of the test section.
No turbulent bursting occurred at X=40 inches for velocity ratios less than 3.18. It should be noted that the corresponding statie wall-jet in each case was turbulent in less than 10 inches. From qualitative estimates of the intermittency, UjjU~=3.12 and 3.24 were laminar while ratios of 3.66 and greater were fully turbul ent. For U/U~=3. 29, the flow was observed to be just on the laminar side of transition, while UjjU~=3.47 appeared to be just past transition with intermittency slightly greater than 50%.
The cases had the following shape factors and R -t's. eXl
U-JIJ Shape Factor R
exit J CD 4.24 589 4.03 559 3.82 1.59 531 3.66 1.62 508 3.47 1.75 482 3.29 1.92 457 3.24 1.99 449 3.12 1.99 433 0.00 2.05 0
The two highest velocity ratios, 4.24 and 4.03, both had slight overshoots in velocity, so shape factors were not calculated. The shape factors for the other cases are in agreement with the observed intermittency estimates and suggest that transition in the test section occurred for velocity ratios greater than 3.47. For these velocity ratios, the shape factor went down to previous turbulent values, and the velocity profile took on a typical
turbulent shape with high shear near the wall followed by a very gradual increase in velocity to U~. The lower velocity ratios of 3.12, 3.24 and 3.29 never quite attained the free-stream-only shape factor of 2.05 due to increased fullness in their mean velocity profiles, as discussed previously.
To check the effect of free-stream velocity on transition of the
augmented flow while holding the slot height at 0.031 inches, 1I ~ was changed from the baseline of 8.45 ftjs to 12.9 ftjs. Velocity profiles at X=40 inches were then measured for U.jU =0.00, 2.09, 2.22, 2.35, 2.50 and 2.65.
J ~
A higher free-stream velocity was desirable but not attainable due to premature transition of the flow near the end of the test section.
The mean velocity profiles, plotted in Figure 31, show that U.jU =2.09 J ~ and 2.22 had laminar profiles nearly identical to the free-stream boundary
layer case, while UjjU~=2.35 had begun to exhibit turbulent properties and was more full near the wall. The final two velocity ratios had gone past transition as evidenced by the typical turbulent velocity profil es. It was noted that no turbulent bursts occurred for Ujjll~ less than 2.31, while the wall-jet component of the augmented flow was turbulent within 7 inches of the exit plane for all velocity ratios.
The R 'tlS and shape factors associated with these cases, tabulated
eXl
on the next page, confirm the mean profile observations and qualitative intermittency estimates made during the data run. Turbulent bursting was observed 30 to 50% of the time for U.jU =2.35 indicating that this case was
J ~
near transition and the shape factor of 1.79, just above the calculated transition shape factor of 1.74, confirmed this.
