Jtam.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

47, 4, pp. 797-814, Warsaw 2009

INFLUENCE OF THE NEGATIVE AND POSITIVE JET OF

WAKE ON LAMINAR-TURBULENT TRANSITION IN

A BOUNDARY LAYER

Jacek Żabski
Zygmunt Wierciński

The Szewalski Institute of Fluid-Flow Machinery PAS, Gdańsk, Poland

e-mail: zw@imp.gda.pl; jaz@imp.gda.pl

In this paper, the results of experimental investigations relating to the
influence of negative and positive jet of the wake on laminar-turbulent
transition in the boundary layer on a flat plate are described. Using the
technique of phase averagingandwavelet analysis, the investigationswe-
re carried out in an aerodynamic tunnel with a low level of turbulence
in the external stream. The existence of serious differences was noted
between the influence of the negative and positive jets due to strong ve-
locity impulses appearing in the area behind the negative jet in the place
of the local minimum of the velocity. However, behind the positive jet
such strong disturbances appear later, not directly in the region behind
the jet. These impulses do not show any signs of chaos and fortuity, the-
refore they should be rather classified as determined disorder.Moreover,
the region of calm behind the positive jet, well-known in the literature,
remains also in the area of entirely disturbed flow.

Key words: laminar-turbulent transition, influence of wakes, flat plate

1. Introduction

The wakes from blade rings are inherently connected with the internal flow
in turbomachinery changing severely flow conditions through following blade
rings. Theyparticularly cause earlier inception of the laminar-turbulent trans-
ition (LTT), which affects, in turn, decidedly the friction on the surface of the
blade and the heat transfer between the flow and blades.
The wake can be differently perceived, depending on the choice of the co-

ordinate system, as a defect of velocity or as a jet. And so it can be treated
as the defect of velocity in the absolute system of co-ordinates connected with



798 J. Żabski, Z. Wierciński

the motionless casing of the machine, that is, the area of reduced velocity in
relation to the mean velocity, while it can be seen as the jet in the system of
co-ordinates bounded with the mean velocity of the flow. If the wake is cut
by a moving blade (at a certain angle to it), which takes place in a fluid-flow
machine, then the boundary layer on the blade is affected by a positive jet
when the speed of the jet is orientated towards the surface of the blade, and
by a negative jet, if the velocity of the jet is directed from the blade towards
the external flow.
We can still make an additional distinction between the influence of the

negative and positive jets on the pressure and suction side of the blade. The
influence of the negative jet on the suction side and the positive jet on the
pressure side of a blade in a rotor in the case of compressors is illustrated in
Fig.1a. It is inversely in turbines, Fig.1b, where the positive and negative jets
affect the suction and pressure side of the rotor blade, appropriately.

Fig. 1. Positive and negative jets of wakes in a compressor (a) and in a turbine
stage (b) (Wierciński, 1999)

The question of the wakes influence on flow in the blade-to-blade passage
of turbomachines has already had a long history. It will be sufficient here to
mention the reviewwork ofMayle (1991). However,manyquestions still rema-
in unrecognized and, in particular, the influence of the positive and negative
jet on the boundary layer and the interaction of the leading edgewith awake.
The kinematics of wake convection through a blade passage was the sub-

ject of many investigations. Meyer (1958) in his work first used the notion of
jet to describe the impact of the wake on the blade surface. He distinguished
the sucking and impinging effect of the jet on the plate surface. Next, Kerre-
brock and Mikolajczak (1970) investigated the wake transport process in the
blade-to-blade passage in the transonic compressor. The motion of the wake
in the blade passage in the direction of the pressure side of the blades was the
reason for the non-uniformity of the temperature field behind the stator. The



Influence of the negative and positive jet... 799

above authors did not use the notion of the jet coined byMeyer (1958). In the
observationsmade byBinder et al. (1984) in the experiment on a one-stage air
turbine the wake was transported in the opposite direction. Probably Hodson
(1985) was the first to use the words ”negative jet” to describe the jet applied
byMeyer to describe the feature of thewake as the difference between theme-
an flow and velocity defect. Most of the investigations on the wake behaviour
in the blade passage were devoted to kinematics and flow structures betwe-
en the blades. The impact of the impinging and sucking effects of the jet on
the laminar-turbulent transition were not considered (Schobeiri and Pappu,
1997). In the paper by Addison and Hodson (1990) there is a suggestion that
the negative jet has a very little effect on the boundary layer which remains
either laminar or turbulent.Wierciński (1995) for the first time described the
different influence of the impinging and sucking effect of the jet on the boun-
dary layer transition. He used the designations ”the positive” and ”negative
jet” in the description of the impinging and suction effects of the wake. In the
experiment, a single rod was employed to generate a harmonic wake which
coming onto the plate caused the negative and positive jet alternately. Behind
thenegative jet thefluctuation level is greater than the onebehind thepositive
jet, (Wierciński, 1995, 1999). Jeon et al. (2002) carried out the investigation
of the transition in the boundary layer on the NACA 0012 profile inserted
in the squirrel cage. They reported that for the counter-clockwise rotation of
the squirrel cage the wake induced turbulent patches grew more quickly and
merged with each other further upstream than those for the clockwise motion
of the squirrel cage. After the consideration of their experimental set up it is
clear that in the terminology of the negative and positive jet it means that
the earlier transition inception in the boundary layer of NACA 0012 profile
appears for the negative jet. Stieger and Hodson (2005) presented the results
in which the transition process in the boundary layer induced by wakes is
affected by the jet that can deform the boundary layer.

There are also some papers devoted to numerical analysis of the wake
convection in blade-to-blade passages, e.g. Dawes (1992), Korakianitis (1991).

Generally, in most numerical and experimental works the influence of the
negative and positive jets on the LTTwas not considered.

The differences in the influence of the negative and positive jet with the
boundary layer in the process of laminar-turbulent transition with strong di-
sturbances behind the negative jet were reported for the first time in the
presentation by Wierciński and Żabski (2007).

The reported beneath research is aimed at investigation of the differences
in the influence of positive and negative jets on the boundary layer on a plate



800 J. Żabski, Z. Wierciński

at zero pressure gradient along it and at a low intensity of turbulence in the
external stream. It is well known that the increased turbulence level is the
reason for the so called by-pass transition, i.e. for overlapping when analysing
the appearance of the Tollmien-Schlichting waves in the boundary layer. The
understanding of the boundary affected by the jets (positive and negative)
should give us some tools for better modelling of non-stationary phenomena
in flowmachines and the laminar-turbulent transition in particular.

2. Experimental stand and programme of investigations

Themeasurements were conducted in a low subsonic wind tunnel with a low
level of turbulence, Tu¬ 0.08%and themaximumspeedof flow U =100m/s.
The measurement chamber with octagonal section had the following dimen-
sions (width, height, length) 600× 460× 1500mm. The boundary layer was
studied on the upper surface of the flat plate of 600×700×14 (width, length,
thickness), Fig.2. The plate was cut at an angle 30◦ and the leading edge
rounded with a radius of 2mm. The incidence angle of the plate was almost
zero, and so the gradient of pressure close to zero value was characterised by
the coefficient of acceleration K = 7 ·10−8. The boundary layer for the case
of flow without wakes was laminar for almost entire length of the plate with
first signs of transition further downstream than Rex > 6 ·105. A round rod
of 3mm diameter and 600mm length served as the wake generator. The rod
was placed at the end of a rocker arm of length 190mm(four bar linkage) and
movedupanddownwith frequency f =4Hz,which gives theperiod 0.25s for
onenegative andonepositive jet.The time-phase of the rodmotion generating
the negative jetwas recorded and themoment of timewas chosen as the phase
mark, when the axis of the rod was at the same height as the leading edge of
the plate. At this place, the velocity of rod is about 2.6m/s. The upstream
distance between the rod and leading edge is equal to L = 86mm, so the
ratio L/d≈ 28.7.While the phasemark is being recorded, thewake produced
by the rod moves at the flow speed, so the trace of negative jet is delayed in
relation to the phase mark (on wavelet graphs – perpendicular bright lines).
The more distant is the traverse from the leading edge, the more delayed is
the registered trace with respect to the phase mark.
Themeasurementswere carried out bymeans of theStreamLine termoane-

mometry systemwith the StreamWare 3.41.20 software and the probe 55P15
of DANTEC. The data was sent to the computer by the acquisition card
NI6040E. The measurements were accomplished for the air velocity coming



Influence of the negative and positive jet... 801

Fig. 2. Experimental stand, 1 – rod in motion as a wake generator, 2 – plate

on the plate U = 15m/s, at the zero incidence angle and for eight various
distances from the leading edge x = 165, 215, 255, 295, 325, 365, 560 and
650mm, which corresponds to the Reynolds numbers Re = 168843, 216979,
257412, 298640, 334414, 374159, 587243, 686918. Themeasurements of the ve-
locity profiles were as a rule performed in a relatively great number of points
from110 to 160 across the boundary layer (perpendicular to theplate surface).
The velocity registration at every point took t=10s and was sampled at

frequency f =5kHz.The final distance of the last point of the velocity profile
from the plate surface was determined by means of the so-called hydraulic
zero method. The time-averaged velocity profiles were determined first, other
parameters characteristic for the boundary layer, such as the thickness of the
layer δ, the coefficients of local friction Cf and so on, were derived as well.
The use of the so-called phase-averaging procedure was a farther step in the
investigation. Single periods of the velocity ensemble were put one on another
and the averaging along the matching points was calculated. Thus, it was
possible to obtain a single period of velocity time trace with lesser random
disorders of duration equal to t=0.25s. The next point of the study involved
wavelet analysis using theMeyer wavelet.

3. Investigation results

3.1. Time and phase averaged

The investigation of the boundary layer started with time averaged me-
asurementswhich yielded results comparablewith those presented in thework
by Wierciński (1999) and Kaiser (2005). The distribution of the local fric-
tion coefficient Cf is presented below as an example, Fig.3. In Figs. 4, 5



802 J. Żabski, Z. Wierciński

and 6, the phase averaging outputs are presented. They are time traces of
velocity in three sections corresponding to the following Reynolds numbers
Rex = 168843, 334414 and 686918. The traverses refer to the first, fifth and
eighth point in Fig.3.

Fig. 3. Distribution of the local shear stress coefficient Cf versus Rex

Fig. 4. Phase averaged time traces of velocity, Rex =168853

To make the visual perception easier, some of the lines were removed,
especially those lying outside the boundary layer, some in the mid region
and these lying close to the wall, where the thermal influence of the plate
was observed. Time on these graphs is dimensionless t/T , where T is the
period of jets equal to T = 0.25s. There are two strong velocity defects -
considered from left to right are negative and positive jets, respectively. For
Rex = 168843, Fig.4, at the very beginning of transition the time traces are
of a smooth shape, though some disorders appear just behind the negative jet.
Further, for Rex =334414 (Fig.5). the zone of disorders widened within the



Influence of the negative and positive jet... 803

Fig. 5. Phase averaged time traces of velocity, Rex =334414

Fig. 6. Phase averaged time traces of velocity, Rex =686918

whole range of time between the negative and positive jet. It looked different
between the positive and negative jet. There is a becalmed region spreading
from the positive jet to almost the middle of the time distance between the
jets. Finally, one deals with a fully turbulent flow, Fig.6, when the negative
jet is hardly visible and the positive one holds on.Thebecalmed region behind
the positive jet also persists, but it is rather short. The phase averaging could
decrease the overall level of fluctuations and smoothed the traces but it was
impossible to damp the fluctuations to zero, especially behind the negative jet
where the disorder was not fully chaotic.
What can be immediately noticed at the first glance is the difference be-

tween the velocity character behind the negative andpositive jet. The velocity



804 J. Żabski, Z. Wierciński

time traces reveal much smoother character behind the positive jet, whereas
behind the negative jet they aremuchmore disturbed, Figs.4 and 5. This can
provide an evidence that the negative jet has amuch stronger influence on the
process of turbulence inception in the boundary layer than the positive one.
In the third of these figures, i.e. in Fig.6, the turbulent flow can be seen in its
full shape and beauty.All the time the traces are disturbed, the negative wake
is hardly visible – it washes away in the surrounding turbulence. It is intere-
sting, however, that the positive wake lasts continually and the time traces
clearly become smooth in the becalmed region, there are no high frequency
fluctuations on the declining part of the trace behind the positive jet. It looks
like a trial to return to the laminar flow.
Continuing the analysis of theflowchange in the boundary layer in relation

to the phase movement – the oncoming wakes – one can raise the question:
what would the phase averaged velocity profile be like at a different moment
of non-dimensional time, such as different sections in Figs.4-6? Only two of
them – from among many – are presented here, see Figs.7 and 8. They are
put in an order corresponding to the two thick straigth lines in Fig.4, i.e. for
the moments of the non-dimensional time τ =0.06 and 0.12. Obviously, they
are not simple time averaged velocity profiles, but the phase averaged velocity
profiles in two differentmoments of time. A large diversity of velocity profiles
is visible as a function of the time phase .

Fig. 7. Temporary velocity profile for Re=168843 and τ =0.06

In Fig.7, the character of the velocity profile is turbulent. It is hard to
mark a viscous sublayer according to the equation U+ = y+. It can be said
that the range of thewall law U+ =A ln(y+)+B reaches deeper,much closer
to the wall. Another conclusion can be drawn from Fig.8, namely, the flow
is laminar. The linear range exists but its course is in agreement with the
following relation U+ =Ky+, where K 6=1.



Influence of the negative and positive jet... 805

Fig. 8. Temporary velocity profile for Re=168843 and τ =0.12

In the next part of the report the graph of the local friction coefficient Cf
versus phase time τ is shown.Dependence Cf = f(τ)was introduced inFig.9
for the Reynolds number Rex = 686918, i.e. for the last investigated point
where the flow is almost fully disturbed by turbulence, whereas in Fig.10 the
graphs of Cf = f(Re,τ) for three various Reynolds numbers Rex = 168843,
298340 and 686918 are presented. The spread of changes of the Cf coefficient
evidently rises with the increasingReynolds number, and for Rex =168843 it
oscillates around the value for the laminar flow. Then, for the Reynolds num-
ber Rex =686918 the range of changes becomes considerably larger because
it passes from laminar to the turbulent values and attains itsmaximum some-
where above. Connecting successive values of Cf from eachmeasuring section
(approximately for one value of theReynolds number), it is possible to obtain
two full loops, one for the negative and the other for the positive jet.

Fig. 9. Local friction coefficient Cf = f(τ) for Rex =686918 versus phase time

In the next part of the report themeasurement results of the velocity fluc-
tuation across the boundary layer are presented. In one graph they illustrate
bothfluctuationsmeasured as time averaged and as phase averaged. Thediffe-
rence between the time and phase averaged values can be treated as a random



806 J. Żabski, Z. Wierciński

part of the velocity fluctuation like turbulence. Figure 11 shows the above
discussed parts of velocity fluctuations for Rex =168853, whereas Fig.12 for
Rex =686918.

Fig. 10. Local friction coefficient Cf = f(τ) for Rex =168843, 298640 and 686918

Fig. 11. Distribution of velocity fluctuations for: Rex =168853: time and phase
averaged and turbulent

Fig. 12. Distribution of velocity fluctuations for: Rex =686918: time and phase
averaged and turbulent



Influence of the negative and positive jet... 807

As can be expected, the level of turbulent fluctuations is higher for the
Reynolds number Re = 686918 (Fig.12) than for Re = 168853 (Fig.11)
because the turbulizationprocess of theflowproceeds togetherwith thegrowth
of theReynolds number. But simultaneously, the amplitude of phase averaged
fluctuations grows,which can be connectedwith the process ofwakewidening,
although ingeneral, theamplitudeof velocity inawakegets smaller ifwidening
occurs. Another attempt to explain this process, however, is a possibility of
amplification in the boundary layer.

3.2. Results of wavelet analysis

It is well known that the wavelet analysis is particularly useful for nonsta-
tionary signal analysis, where one deals with signals of different frequencies at
different time intervals. The feature of wavelet analysis is crucially different
from the Fourier analysis, where it is necessary to assume that the analysed
signal is stationary.
Five points in the velocity fluctuation profile were chosen to carry out

the wavelet analysis, i.e. two points lying at the edges of the distribution
and three characteristic points of the distribution of the velocity fluctuation,
two maximal and one local minimum. The point at the outside edge of the
distributiongoes beyondconventional borders of the layer, that is U =0.99U0,
because the velocity fluctuations are well seen outside this border, and this
point denotes the areawhere the velocity fluctuation does not become smaller
any more and are actually equal to the velocity fluctuation in the outside
stream. It is obvious that thepoints couldbe found inadifferentway.However,
in this paper, for the presentation purpose only one pointwas chosen as closest
to the plate surface where the thermal influence of the plate on the velocity
measurements was not observable, so it is usually the point in the range of
y+ =10-13.
The following seven graphs were presented for the subsequent Reynolds

numbers. Every graph is built in a similar way. The velocity time trace is pre-
sented in the first subgraph at the top, usually somewhat above three periods
of the wake. The second central subgraph shows the results of the wavelet
analysis of the records from the first subgraph, thus the values of wavelet coef-
ficients a for a given frequency and time. The graph is three-dimensional but
the altitudes are given as isoheights in shades of greywith shadebarwith scale
on the right side. They are vertical bright lines in the figures. Every line points
out a negative jet. Amongnegative jets, there are obviously positive ones. The
bright horizontal line denotes the frequency f =192Hz.The values of wavelet
coefficients for this frequency are introduced in the third lowest subgraph.The



808 J. Żabski, Z. Wierciński

wavelet coefficents a are indicated on the vertical axis of this graph, whereas
the time t is given on the horizontal axis like in the two preceding graphs.
In the first of these graphs, Fig.13, it is possible to see some considera-

ble velocity distortions in the time-interval just after passing the negative jets
in the form of a series of velocity impulses, usually two or three velocity di-
sturbances. Such disturbances are not observed behind the positive jets. They
appear behind the negative jet in the area of the local velocity minimum.Mo-
reover, two characteristic wave trains of frequencies f =42Hz and 192Hz in
the time-intervals between wakes are seen. The intensity of the wave of frequ-
ency 192Hz is considerably larger behind the negative jets than the positive
one, which can be observed in the third subgraph, Fig.13. The secondwave of
frequency 42Hz in principle appears with practically equal intensity behind
both negative and positive jets.

Fig. 13.Wavelet chart, Rex =168843, Y+ =10

In Fig.14, for Re= 216979, the increasing disturbances behind the nega-
tive jet can be seen, and apart from single impulses also a series of impulses
is practically bounded with each other. Moreover, some intensive impulses of
velocity occur in the area close to the half of the range between the negative
and positive jets, which seems to be novel, and the impulses are not tied up
with the impulses behind the negative jet alike. The intensity of the wavelet
coefficients for the frequency f = 42Hz diminishes, while the occurrence of
wave-trains about the frequency f =192Hz widens.



Influence of the negative and positive jet... 809

Fig. 14.Wavelet chart, Rex =216979, Y+ =10

Fig. 15.Wavelet chart, Rex =257412, Y+ =10

In Fig.15, with respect to the Reynolds number Re = 257412, one can
observe that the intensity of impulses behind the negative jets grows, like
the intensity of a single impulse in the half of the area behind some negative
jets. The level of disturbances behind the positive jets is still small, and the



810 J. Żabski, Z. Wierciński

becalmed region is especially well visible. However, some disturbances begin
to appear before the negative jets and the intensity of these disorders – aswill
be seen farther – will rise.

In Fig.16, regarding the Reynolds number Re=298640, a farther growth
of disturbances past the negative jets can be easily noted, and even the
first large impulses of the velocity appear on the background of the incre-
asing level of disturbances in the area before the positive jets. Neverthe-
less, there is another region without disturbances directly behind the posi-
tive jet. Thus, the zone called the becalmed region remains firm. The de-
scribed symptoms can, of course, be observed in the three diagrams. In the
upper diagram the time traces show the number of impulses continuously in-
creasing, whereas in the central diagram the full wavelet spectrum from 32 to
1050Hz illustrates the rising number of distortions. Finally, in the third dia-
gram, a section for frequency f = 192Hz also shows a larger level of distur-
bances.

Fig. 16.Wavelet chart, Rex =298640, Y+ =10

InFig.17, for theReynolds number Re=334414, the tendencies described
for Fig.16 keep on, that is, the number of strong velocity impulses grows
behind the negative jets. The becalmed region behind the positive jets still
holds and the number of strong impulses before negative jet rises.



Influence of the negative and positive jet... 811

Fig. 17.Wavelet chart, Rex =334414, Y+ =10

Furthermore, in Figs. 18 and 19 for the Reynolds numbers Re = 374159
and 686918, the area behind the negative jets is entirely filled with strong
impulses of the velocity, whereas the emphasised becalmed region past the
positive jet holds on.

Fig. 18.Wavelet chart, Rex =374159, Y+ =12



812 J. Żabski, Z. Wierciński

Fig. 19.Wavelet chart, Rex =686918, Y+ =12

4. Conclusions

The results of the experiment presented in the work show a fundamental dif-
ference of the influence of the negative and positive jet on the boundary layer.
A strong distortion in the form of velocity impulses is revealed in the area just
behind the negative jet for the lowest value of theReynolds numbermeasured
in the experiment. These disturbances are observed in the region of the local
minimum of velocity. The decrease of the pressure in the negative jet can be
very likely responsible for the appearance of these disturbances. There are no
such disturbances behind the positive jet which can be explained by the pres-
sure rise in the positive jet.With the growing Reynolds number, the quantity
of these impulses grows and they join in larger structures, the most probably
in the spots of turbulence, but they clearly still differ from the jet (wake). It is
possible to say that the character of these disturbances is not entirely chaotic
and rather deterministic.
Next, the impulses of velocity appear suddenly in the half of the distance

between the negative and positive jet. Their character can be supposed as the
turbulent spot of natural transition probably not connectedwith the influence
of wakes (jets). However, the becalmed region, which is distinctively visible
behind the positive jet still holds on, whereas such a becalmed region passes
unnoticed behind the negative jet. Themore the zone behind the negative jets



Influence of the negative and positive jet... 813

is filled upwith strong impulses, the greater is theReynolds number.Thus the
becalmed region persists in the final Reynolds number reported in the present
work.
Additionally, theharmonicwave trains of frequencies of f =42and 192Hz

in the regions between both jets are observed. And these wave trains are not
visible outside the boundary layer.
Moreover, the measurements of the distribution of the phase averaged ve-

locity across the boundary layer show that the viscous sublayer is probably
much smaller in the area of the wake than in the turbulent boundary layer
withoutwakes. Furthermore, beyond the area of thewake, even if the laminar
boundary layer of the linear type U+ =Ky+ is considered, the coefficient K
is rather different from unity.

References

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814 J. Żabski, Z. Wierciński

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indukowane śladami spływowymi, IMP PAN, ZN 499/1450/99, Gdańsk, DSc
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15. Wierciński Z., Żabski J., 2007, Phase averaged characteristics of the boun-
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Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, Italy

Wpływ ujemnego i dodatniego strumienia śladu spływowego na przejście

laminarno-turbulentne w warstwie przyściennej

Streszczenie

W pracy przedstawiono badania eksperymentalne dotyczące wpływu ujemnego
i dodatniego strumienia śladu spływowegona przejście laminarno-turbulentnewwar-
stwie przyściennej na płaskiej płycie. Badania przeprowadzono w tunelu aerodyna-
micznymoniskimpoziomie turbulencji przepływuzewnętrznego,wykorzystując tech-
nikę fazowego uśredniania i analizy falkowej. Stwierdzono istnienie poważnych różnic
międzyoddziaływaniemujemnego i dodatniego strumieniawpostaci silnych impulsów
prędkości pojawiających się w obszarze za ujemnym strumieniem w miejscu o lokal-
negominimum prędkości. Za dodatnim strumieniem takie silne zaburzenia pojawiają
się później i nie bezpośrednio za nim. Ponadto regiony uspokojenia za dodatnim stru-
mieniem, dobrze znane z literatury, są dobrze widoczne także w rejonie całkowicie
zaburzonego przepływu.

Manuscript received July 10, 2008; accepted for print May 11, 2009