CC BY
12
UDC
J. ZABSKI
Institute of fluid-flow machinery polish academy of sciences, Gdansk
VELOCITY WAVES IN THE BOUNDARY LAYER DISTURBED BY WAKES OF NEGATIVE AND POSITIVE JETS IN ACCELERATING FLOW
Experimental boundary layer investigation was performed for two values of velocity acceleration at the edge of layer-. The flow was disturbed by oncoming wakes from a pendulating upstream rod yielding negative and positive jets in turn (negative jet if the rod goes upwards making suction in boundary layer on the upper surface of the flat plate, positive jet — the rod goes downward). Velocity traces and phase-averaged velocity traces were obtained using periodic phase mark. Mean velocity profiles and longitudinal distribution of mean or integral parameters stayed close to laminar pattern. The shape of wakes on velocity traces were these same regardless of jet direction. However-, past negative jets velocity waves were observed on velocity traces. They were placed in the damped region of Tollmien-Schlichting waves. Past positive jets there was no evidence of velocity waves, which is main difference between influence of both kind of jets on boundary layer development.
Key words: boundary layer, wake, wave, negative jet, positive jet, phase-averaged, velocity traces.
Introduction
Unsteady boundary-layer flows over the blades of turbines and compressors contribute to the loss and heat transfer to the blades. Particularly it is responsible for earlier laminar-turbulent transition. In multistage turbomachinery upstream blades shed wakes on following ones. The process of wakes action that impinge on blade surfaces is periodic. The wake can be identified as velocity deficit in the stationary frame, whereas as a jet in the frame relative to the mean flow. The jet is consider as a positive or negative one depending on jet vector sign. Jet with vector pointing surface is called positive one. The negative jet is considered inversely.
Tollmien-Schlichting velocity waves in boundary layer flows are well known, however their presence in the flow disturbed by strong wakes a bit less. Generally influence of jet sign direction — negative or positive on boundary layer development is not clearly distinguish by many researchers. The first author who noticed this difference between negative jet which causes suction in boundary layer and a positive jet which makes enlarged pressure was Meyer [1], Fig. 1. Wakes of negative jets make earlier laminar transition which was probably for the first time reported by Wiercinski [2] and then confirmed in detail by Zabski [3] who observed diffusion of turbulence form negative jets. However some reports, for instance Jeon et al [4], also indicate a difference of wakes direction with respect jet orientation towards the surface, but it was no stated explicitly. Consideration of their
© J. Zabski, 2013
experimental setup leads to conclusion that their counter-clockwise rotation of the squirrel cage gives negative jets in terminology of this paper. In the same manner their clockwise rotation should give positive jets. Of course not every flow disturbed by wakes is driven to full turbulence. There can exist calm region between them if the frequency of wakes generation is low. In some circumstances this region can originate waves as reported by Stieger [5] who identified them as TS waves. This paper describes appearance of small waves in accelerating (which is an enhancement of previous paper [6]) flow behind a wake of negative jet. It is significant feature as there is no clear evidence of waves past positive jets.
Measurements were carried out in a subsonic wind tunnel of low turbulence level that did not exceed Tu = 0.08% and the flow in free stream of front of test section was U= 15 m/s. Dimensions of the test section were 600x460x1500 mm (width, height, length) and the corners were chamfered. Scheme of the test chamber, a flat plate and a pendulum mechanism is shown in Fig. 2. The plate width, length and height are: 600x700x14 mm respectively. The leading edge was rounded with a radius 2 mm. The incidence angle was adjusted and for this measurement amounted a = -2.44o and -0.44o. That corresponds to flow acceleration over upper surface of the flat:
and К = 9.96 10 8 respectively,
where: dU — velocity gradient along the plate .
dx
Fig. 1. Wake as a negative (Low Pressure) positive (High Pressure) jet in the boundary layer Exeprimental rig and instrumentation
That means that for smaller angle the flow was of nearly at constant velocity. Wakes were generated by means of a rod of 3 mm diameter which moved up and down by means of pendulum mechanism mounted in front of the plate. The rod movement frequency equaled to f = 4 Hz what gives a period of T = 0.25 s for one negative and one positive jet. The non-dimensional parameters of wake generation are Strouhal number and F coefficient:
fC
Sr = — = 0.19 , U
Ф = -U- = 5.74
Ub '
(2)
(3)
where: C — plate length, f — frequency of wakes generation, Ub — rod maximal velocity when it is at the same height as leading edge of the plate.
The measurements were made by means of StreamLine thermoanemometry system with the StreamWare 3.41.20 software and the probe 55P15 DANTEC . The data were recorded via 12 bit NI 6040E acquisition card. The sampling rate was 5 kHz . In order to synchronize hot-wire output with passing wakes for farther phase-averaging of velocity traces procedure (Dong and Cumpsty call it ensemble averaging [7], other authors call it phase-lock) a mark signal was recorded when the rod was going up and was in equal height with the leading edge of plate . Sample duration amounted to t = 10 s for each point of velocity profile. Time averaging was used to obtain mean values of velocity and fluctuations profiles as well as longitudinal parameters derived from them: skin friction coefficient, shape coefficient, boundary layer thickness and so on . Phase-averaging yielded velocity traces filtered from random disturbances. This was done by averaging phase matching points of real time velocity traces. The duration of each phase-averaged velocity trace was t = 0.25 s and that is one period of one negative and one positive jet passing . Farther non-dimensional period t = 1 is used for phase-averaged traces . Measurement traverses were located at distances from the leading edge: x = 165, 215, 255, 295, 335, 365, 560, 650 mm which corresponds to Rex = 165677, 218600, 258355, 303167, 339593, 367920, 570338, 657117 (K =9.96-10"8, a = -0.44o) . For higher pressure gradient (K=3.3610-7): x = 295, 335, 365 mm, Rex = 277718, 317720, 346604. Each traverse consisted of at least 100 points.
Fig. 2. The flat plate and wake generator 1 — a thin rod generating wakes, 2 — a flat plate
1. Results
Time averaged results were typical. Only skin
friction coefficient distribution is shown in Fig. 3.
Although flow was strongly disturbed by oncoming wakes mean-time parameters remain rather lami-
nar, the same refers to mean velocity profiles, not
shown in this paper. Only mean velocity fluctuation
u'/U profiles reveal presence of wakes — a second
a peak value in the outer zone of layer.
Fig. 4 and Fig. 5 show phase-averaged velocity traces versus non-dimensional period for the distance from attack edge x = 365 mm for two values of accelerating flow coefficient K. There were more charts for earlier mentioned travers locations, but they were similar to those from Fig. 4, and are not presented here.
Fig. 3. Skin friction coefficient distribution
The upper traces are taken at the edge of layer, the lowest ones are in the close vicinity of wall —
viscous sub-layer. First strong velocity defect is due to negative jet, second — positive one. Traces behind the positive jet are much smoother than traces following the negative jet. For the flow at K = 9.96 10-08 (a = -0.44o) there are velocity waves behind the negative jet. They occupy whole mid-jet area or only a part. In Fig. 4 they begin shortly after the negative jet and reach the centre of calm region between wakes. The waves in Fig. 5 (K = 3.36 10-07, a = -2.44o) seem to have bigger magnitude and they are concentrated in narrow belt around centre of calm region between wakes. In both cases the waves shown start at the vicinity of wall — traces of lowest velocity — and end up at about U = 12 m/s. Fig. 6 shows waves range in velocity profile. They end up in a trough between fluctuation peaks. That may indicate dumping effect of external turbulence, taking into account that second peak in velocity mean fluctuation profile is supposed to be evoked by wakes.
Fig. 4. Phase-averaged velocity traces for slightly accelerating flow K=9.96E-0
Rex=367920
Fig. 5. Phase-averaged velocity traces for accelerating flow K=3.36E-07, Rex= 346604
Some measured frequencies are marked with their A values to better locate them against neutral curves . Taking this into account all frequencies lie in the region of damp frequencies . If fact there was no laminar-turbulent transition for described
flows . The data in Fig . 7 reveals some scatter that depended on which trace was chosen for frequency counting . It seems the real range is wider and spectral analysis is indispensable . Also magnitudes should be investigated.
2. Conclusions
Wake-induced transition in boundary layer flow along a flat plate was experimentally investigated. The wakes were generated by pendulating cylinder yielding negative and positive jets by turns on investigated surface of the plate. Two incidence angle of plate were used yielding one slower and one faster accelerating flow given by K coefficient.
Mean-time velocity profiles and longitudinal parameters (Cf, 8, H) distribution remained close to laminar ones. Only mean-time fluctuation velocity profiles differed from laminar pattern. Second peak in outer zone of boundary layer is an evidence of wakes influence of boundary layer.
Phase-averaged profiles are smooth except regions of wakes. There is no merging of wakes observed and their width grows slowly. The mid-wake region remained laminar and no turbulence diffusion form wakes was noticed.
Behind wakes of negative jets little magnitude waves developed till next wake — wake of positive jet. The waves occupied the whole mid-wakes area or only part. Careful track of velocity traces shows waves origin close to the wall and final damping at a height where a depression between peaks on mean fluctuation is located. When a wake of positive jets passes no clear evidence of waves is observed.
Farther study with application of Fourier analysis is desirable. Another important issue is explanation of waves presence only past negative jets.
References
1 . Meyer R. The Effect of Wakes on the Transient Pressure and Velocity Distributions in Turbomachines / R.Meyer // Trans.Journal of Basic Engineering . - 1958 . - No (80) . -P . 1544-1552.
2 . Wiercinski Z.The Influence of the Periodic Wake Behind a Cylinder Pendulating in the Cross-Stream Direction on the LaminarTurbulent Transition in the Boundary Layer of a Flat Plate / Z . Wiercinski // Proc . Conf. Unsteady Aerodynamics and Aeroelasicity of Turbomachines . - 1995. - P. 461-479.
3 . Zabski J .Wplyw gradientu cisnienianaprzejscie laminarno-turbulentne w aerotermicznej warstwie przysciennej / J . Zabski - Gdansk: Instytut Maszyn Przeplywowych Polskiej Akademii Nauk, 2009.
4 . Jeon W. Experimental study of boundary-layer transition on an airfoil induced by
periodically passing wake / W. Jeon, T . Park, S . Kang // Experiments in Fluids . — 2002. — No (32) . - P. 229-241.
5 . Stieger RThe Effect of Wakes on Separating Boundary Layers in Low Pressure Turbine / R.Stieger — Cambridge: Cambridge University Engineering Department, 2002.
6 . Zabski J. Small Disturbance Waves in Boundary Layer Induced by Oncoming Wakes / J.Zabski // Colloquium FLUID DYNAMICS Prague . — 2012 .
7 . Dong Y. Compressor Blade Boundary Layers: Part 2 - Measurements with incident wake / Y . Dong, N. Cumpsty // Journal of Turbomachinery. — 1990 . — No (112) . — P. 231-240.
8 . V. Lev enko Charakteristiki ustojivosti pograninych sloev / V. Levenko, A. Volodin, S.Gaponov, Sibirskoe Otdelenie, Novosibirsk, 1975.
Submitted to the editorship 11.07.2013
Жабски Яцек. Волны скорости в пограничном слое, возмущенном спутными следами положительных и отрицательных струй в ускоряющемся потоке
Рассматривается экспериментальное исследование пограничного слоя для двух значений ускорения потока на его границе. Течение возмущено проходящими следами от колеблющегося выше по потоку стержня, создающего положительные и отрицательные струи поочередно (отрицательная струя — если стержень движется вверх, создавая разрежение в пограничном слое на верхней поверхности пластины, положительная — если стержень движется вниз). Траектории и осредненные по фазе траектории получены с помощью периодических фазовых меток. Профили средней скорости и продольные распределения средних или интегральных параметров оставались близкими к ламинарному виду. Форма следов на траекториях скорости была такой же, независимо от направления струи. Однако, в траекториях скорости наблюдались волны, вызванные прохождением отрицательной струи. Они размещались в затухающем диапазоне волн Толмина-Шлихтинга. После положительных струй волны скорости не наблюдались, в чем и проявляется основное различие влияния обоих видов струй на развитие пограничного слоя.
Ключевые слова: пограничный слой, след, волна, отрицательная струя, положительная струя, фазовое осреднение, траектории скорости.
Жабски Яцек. Хвил швидкост в пограничному шар1, збуреному супутними с.пдами позитивних 1 негативних струмешв у потощ, що прискорюеться
Розглядасться експериментальне досл1дження примежового шару для двох значень прискорення потоку на його гранищ. Теч1я обурена прох1дними сл1дами в1д стержня який коливасться вище за потоком, що створюс позитивы I негативш струмеш по черз1 (негативна струмть - якщо стержень рухасться вгору, створюючи розр1дження в при-межовому шар1 на верхшй поверхш пластини, позитивна - якщо стержень рухасться вниз). ТраскторП I осереднеш за фазою трасктори отримаш за допомогою перюдичних фазових мток. ПрофШ середшй швидкост1 I поздовжш розподыення середшх або ттегральних параметр1в залишалися близькими до лам1нарного вигляду. Форма сл1д1в на трасктор1ях швидкост1 була такою ж, незалежно в1д напрямку струменя. Однак, в трасктор1ях швидкост1 спостергалися хвил1, викликаш проходженням негативного струменя. Вони розмщувалися в згасаючому д1апазош хвиль Толмта-Шл1хттга. Шсля позитивних струмешв хвил1 швидкост1 не спостержалися, в чому I проявляеться основна в1дмтшсть впливу обох вид1в струмешв на розвиток примежового шару.
Ключов1 слова: примежовий шар, сл1д, хвиля, негативний струмшь, позитивний струмть, фазове осереднення, трасктори швидкост1.
