Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple
This study is to investigate the details of the average and unsteady flow structures in front, inside and downstream of the shallow spherical and cylindrical dimple placed on a flat plate at the different distances with different pre-dimple boundary layer thicknesses. A comparison of both spherical...
Збережено в:
| Опубліковано в: : | Промышленная теплотехника |
|---|---|
| Дата: | 2006 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут технічної теплофізики НАН України
2006
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/61435 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple / A. Khalatov, A. Byerley // Промышленная теплотехника. — 2006. — Т. 28, № 5. — С. 5-15. — Бібліогр.: 23 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859467855860334592 |
|---|---|
| author | Khalatov, A. Byerley, A. |
| author_facet | Khalatov, A. Byerley, A. |
| citation_txt | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple / A. Khalatov, A. Byerley // Промышленная теплотехника. — 2006. — Т. 28, № 5. — С. 5-15. — Бібліогр.: 23 назв. — англ. |
| collection | DSpace DC |
| container_title | Промышленная теплотехника |
| description | This study is to investigate the details of the average and unsteady flow structures in front, inside and downstream of the shallow spherical and cylindrical dimple placed on a flat plate at the different distances with different pre-dimple boundary layer thicknesses. A comparison of both spherical and cylindrical dimple geometric configurations was made to assess their relative benefits.
Досліджено особливості осередненої та нестаціонарної структури потоку перед, всередині і за дрібними заглибленнями циліндричної та сферичної форми, які зроблені на плоскій пластині на різних відстанях від входу, що забезпечує різну товщину пограничного шару набігаючого потоку. Порівняно характеристики заглиблень циліндричної та сферичної форми.
Исследованы особенности осредненной и нестационарной структуры потока перед, внутри и за “мелким” углублением цилиндрической и сферической формы, выполненным на плоской пластине на различных расстояниях от входа, что обеспечивает различную толщину пограничного слоя набегающего потока. Сделано сравнение характеристик углублений цилиндрической и сферической формы.
|
| first_indexed | 2025-11-24T07:56:17Z |
| format | Article |
| fulltext |
INTRODUCTION
The suction side of turbine blades suffers from the
boundary layer separation while operating at low (off;
design) Reynolds numbers. The separation zone
reduces the blade efficiency and leads to a reduction
of turbine power. To improve the turbine efficiency
both active and passive flow control techniques are
now being considered. Amongst the potential passive
techniques are shallow surface dimples (h/D ≈ 0,10)
since they provide reduced profile losses at low
Reynolds numbers [1, 2]. Compared with other pas;
sive techniques (V;grooves; wires), spherical dimples
have demonstrated the best results in terms of reduc;
tion in separation losses and improvements in the
region of a flow reattachment. The best condition for
the flow reattachment creates the turbulent flow pat;
tern both inside and downstream of the dimple [1].
The spherical dimples can be classified based on
their depth to diameter ratio: (a) shallow dimples
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 5
ТЕПЛО� И МАССООБМЕННЫЕ ПРОЦЕССЫ
Досліджено особливості осередне+
ної та нестаціонарної структури потоку
перед, всередині і за дрібними заглиб+
леннями циліндричної та сферичної
форми, які зроблені на плоскій пластині
на різних відстанях від входу, що забез+
печує різну товщину пограничного шару
набігаючого потоку. Порівняно характе+
ристики заглиблень циліндричної та
сферичної форми.
Исследованы особенности осред+
ненной и нестационарной структуры по+
тока перед, внутри и за “мелким” углуб+
лением цилиндрической и сферической
формы, выполненным на плоской плас+
тине на различных расстояниях от вхо+
да, что обеспечивает различную толщи+
ну пограничного слоя набегающего
потока. Сделано сравнение характерис+
тик углублений цилиндрической и сфе+
рической формы.
This study is to investigate the details of
the average and unsteady flow structures
in front, inside and downstream of the shal+
low spherical and cylindrical dimple placed
on a flat plate at the different distances with
different pre+dimple boundary layer thick+
nesses. A comparison of both spherical
and cylindrical dimple geometric configu+
rations was made to assess their relative
benefits.
UDC 532.516:536.24.01
A. KHALATOV1, A. BYERLEY2
1Institute for Engineering Thermophysics, National Academy of Sciences, Kiev, Ukraine
2United States Air Force Academy, Colorado Springs, USA
EFFECT OF PRE+DIMPLE BOUNDARY LAYER THICKNESS
ON FLOW CHARACTERISTICS WITHIN AND DOWNSTREAM
OF A SINGLE SHALLOW DIMPLE
Cf – drag coefficient;
D – dimple projected (surface) diameter, m;
f – frequency of bulk flow oscillations, s–1;
f1 – flow gradient parameter, [ ;
H* – channel height, m;
H – shape factor, / ;
h – dimple depth, m;
L – extent of in;dimple separation zone, m;
ReD – Reynolds number based, U∞ D/ν;
Rex – Reynolds number, U∞x/ν;
SCD – single cylindrical dimple;
Sh – Strouhal number, f D /U∞;
x – distance from test section beginning to dimple
front edge (over centerline), m;
x* – downstream distance from dimple back rim, m;
xD – pre;dimple measurements, m;
U∞ – flow speed in front of dimple, m/s;
z – spanwise distance, m.
Greek symbols:
δ – boundary layer thickness, m;
δ0av – average boundary layer thickness, m;
δ2 – momentum thickness, m;
δ1 – displacement thickness, m;
ν – air kinenatic viscosity, m2/s.
Subscripts:
o – flow parameters in front of a dimple;
oo – flow parameters over a flat plate.
2δ1δ
∞∞ ∂∂ U/]x/U2δ
(h/D≤ 0,06…0,10), (b) deep dimples (h/D>0,2), and
(c) intermediate depth dimples (h/D = 0,1…0,2).
There is no separation inside shallow dimples, where
only Gцrtler vortices exist over a dimple concavity
generating the Karman vortex streets downstream of
the dimple [3 – 6]. Analysis of the Russian data shows
that in the intermediate and deep dimples the
Karman vortex street appears at ReD from 600 to 800
and transforms into the twin vortex pattern between
ReD ≈ 1000 and ReD ≈ 3200. In some cases inside the
intermediate dimple the twin vortex may exist up to
ReD = 100000 [10].
The twin vortex was observed in the intermediate
spherical dimples (h/D = 0,15 … 0,20) in the ReD
range between 3200 and 13000 however this vortex
disappeared between 11000 and 27000 creating the
side;to;side fluctuating vortex [9]. Gachechiladze [7]
has reported the existence of a twin vortex in the
intermediate dimple (h/D = 0,15) up to ReD ≈ 4000;
the weak side;to;side fluctuating vortex appears at
ReD ≈ 4000 to transform into the stable fluctuating
vortex structures by ReD ≈ 5500.
Kesarev & Kozlov [12] have reported the existence
of developed fluctuating vortex structures inside a
deep single hemispherical dimple (h/D=0,5) at high
Reynolds numbers. At ReD > 180000 and low
freestream turbulence, the Strouhal number is 0,08
(16 Hz). At higher freestream turbulence the vortex
fluctuations are suppressed. The Strouhal number is
0,04 (8 Hz) at Tu =15 % and drops to Sh = 0,006
(0,13 Hz) at Tu = 20 % (ReD = 300000).
Furthermore, the external vorticity greatly reduces
the vortex fluctuations inside the dimple. The oscil;
lating flow structures inside the hemispherical dimple
(h/D = 0,5) were also observed in Snedeker and
Donaldson [13] at ReD from 73000 to 320000.
According to Shchukin, et al. [5] a single vortex exists
in the hemispherical dimple (h/D = 0,5 at
ReD = 2260, at ReD = 4520 the vortex periodically
changes the sign of rotation. In the ReD number
range from 9000 to 15500 the vortex transforms into
the side;to;side oscillating pattern.
For an intermediate spherical dimple (h/D=0,13)
the vortex angle slope is around 10 degrees with
respect to a flat plate surface. The vortex structure
persists downstream of a dimple a distance from 1,5 D
to 2,5 D [9]. The analytical solutions and precise flow
visualizations have disclosed “tornado;like” nature of
the side;to;side fluctuating vortex with substantial in;
vortex energy concentration [7].
These conclusions have been reported for the single
spherical dimple with a sharp;edged rim. No side;to;
side oscillating vortices were observed in a deep spher;
ical dimple (h/D = 0,26) with a rounded;off rim [9],
as well as in a deep dimple (h/D = 0,5) up to
ReD = 350000 at the supersonic (M< 4,0) flow [11].
Recent experiments [14, 15] have revealed that
unsteady vortex structures also exist inside and down;
stream of a single shallow spherical dimple
(h/D = 0,1) at relatively low Reynolds numbers
(ReD < 25000). Unlike high ReD numbers, this type of
flow unsteadiness is a bulk flow oscillation discharged
from the dimple due to the in;dimple flow separation.
The weak streamline fluctuations (Karman street type)
downstream of a dimple appear as early as ReD ≈ 3500,
transforming afterwards to bulk flow oscillations. The
maximum of flow fluctuations (f = 13,4 Hz) is at
ReD ≈ 17500, corresponding with a very high Strouhal
number magnitude (Sh = 1,75) indicating the non;
linear correlation between the freestream flow speed
and bulk flow fluctuations.
Cylindrical dimples may be a good alternative to
spherical dimples because of ease of manufacture.
However, over the last few years there has not been
much information added to the cylindrical single
dimple database, which was established over 50 years
ago by Wighardt [16]. The peaks in the drag incre;
ment curve Δ Cf = f (h/D) reflect important changes
in the flow patterns. The minimum extra drag ΔCf
was found for shallow dimples at h/D from 0,1 to 0,2
and h/δo = 0,6. Experimental data of Wighradt has
shown the important role of relative boundary layer
thickness on extra pressure losses. Terekhov, et al. [9]
showed that unsteady flow structures exist inside a
cylindrical dimple. Hiwada, et al. [17] demonstrated
that a heat transfer minimum for both single spherical
and cylindrical dimples is achieved at h/D = 0,2.
The Laser Doppler measurements were performed
by Khalatov, et al. [15] to analyze the flow pattern
after the shallow cylindrical dimple (h/D = 0,1) at
relatively low Reynolds numbers (ReD < 23500).
Based on the boundary layer measurements an impor;
tant conclusion has been made that the laminar;tur;
bulent flow transition downstream of a cylindrical
dimple (h/D = 0,1) occurs somewhere between
ReD = 5200 and 9400.
6 ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
The shallow (h/D = 0,1) cylindrical dimples gen;
erate the bulk flow fluctuations in the downstream
direction at ReD > 3500…4000 with the maximum
Strouhal number Sh ≈ 2,0 reached at ReD ≈ 9350.
The in;dimple reverse flow zone arises at ReD ≈ 3500
and steadily grows with Reynolds number increase. In
addition, cylindrical dimples yield longer separation
zones than spherical dimples given identical flow
conditions. Asymmetrical dimples [2, 18, 19] gener;
ate the fluctuating vortex structures, as well, but addi;
tional investigations are necessary to study this in
more detail.
There is a vast experimental database involving a
rectangular dimpled channel. Ligrani, et al. [20] has
given a brief review of these investigations. As report;
ed [21], in a channel with tight dimple arrangement
the key flow features responsible for the heat transfer
augmentation over an array of dimples are: (a) shed;
ding of multiple vortex pairs from dimples, (b) strong
secondary fluid motions inside vortex pairs, (c)
unsteadiness associated with vortex pair shedding and
in;dimple flows. According to Ligrani, et al. [21], the
vortex structures shed from the dimples become
stronger as the ratio H*/D decreases. A primary vor;
tex shedding frequency of 8,0 Hz and a dimple edge
vortex pair oscillation frequency of 6,5 Hz have been
detected for h/D=0,50 at ReH = 20000 [22]. These
frequencies are consistent with those obtained for the
shallow single spherical and cylindrical dimples [14].
To summarize, the flow unsteadiness is an inherent
flow feature of dimple configurations. The effect of
flow unsteadiness on heat transfer and surface friction
depends on the dimple configuration (spherical;
cylindrical; asymmetrical; others), relative dimple
depth (h/D), Reynolds numbers ReD, and Rex (pre;
dimple boundary layer thickness) numbers, and dim;
ple rim shape (sharp;edged; rounded;off). A litera;
ture survey reveals that there have not been
measurements of flow characteristics downstream of
single dimple at various boundary layer thicknesses
and relatively low Reynolds numbers where the effect
of surface dimples is most significant.
OBJECTIVE
There is a very limited amount of information
in the database for the relatively low flow velocity
regimes corresponding to Rel <25000. The applica;
tion of dimples for the flow separation control
requires fundamental knowledge of the fluid flow fea;
tures for the shallow dimples (h/D = 0,1) with differ;
ent pre;dimple boundary layer thicknesses, simulat;
ing different dimple locations on the turbine blade.
The objective of this study is to investigate the
details of the flow structures in front of, inside and
after a shallow (h/D = 0,1) spherical and cylindrical
dimple placed on a flat plate at different distances
with different pre;dimple boundary layer thicknesses.
The experimental study was performed under low
Reynolds number conditions (ReD < 25000) with a
freestream pressure gradient of zero. This includes
laminar flow pattern in front of the dimple, but both
laminar and turbulent flow regimes after a dimple.
The results presented include the vortex patterns,
in;dimple separation zone extent, unsteady flow phe;
nomena (bulk flow oscillations), velocity profiles, and
details of the laminar;turbulent flow transition down;
stream of the dimples. A comparison of both spheri;
cal and cylindrical dimple geometric configurations
was made to assess their relative benefits.
EXPERIMENTAL FACILITY AND
PROCEDURE
Test section
This experimental program was performed in the
U.S. Air Force Academy (Colorado Springs) closed;
circuit water tunnel (Fig. 1a) – capable of operating
over a speed range of 0,05 m/s to 0,5 m/s with an axial
flow pump capable of producing a volumetric flow
rate of 0,7 m3/s. The test channel is 1830 mm long
with a rectangular cross section (610 mm height;
457 mm width). The sidewalls and floor (bottom) are
made from a glass to allow for flow observation. The
inlet nozzle has a contraction ratio of 6 : 1, the turbu;
lence intensity at the test section inlet is below 1,0 %.
The mean velocity at the inlet is uniform to within
± 2 %, the mean flow angularity is around ± 1,0
degrees in both pitch and yaw directions.
The general design of the test section has been
considered in [14]. The test section (Fig. 1b) is an
acrylic flat plate (19 mm thick) with an elliptically
shaped leading edge (R ≈ 2 m). It is 1220 mm long
and 381 mm wide. Two single cylindrical dimples sep;
arated in the spanwise direction were machined into
the test section at a distance of 88 mm and 264 mm
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 7
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
from the leading edge to the dimple center. Both dim;
ples have the identical projected (surface) diameter of
a dimple by means of a clay used to provide the inner
fillet. The test cases and dimple locations are pre;
sented in Table 1.
The Reynolds number ReD ranged from 3200 to
23500, corresponding to a range of Reynolds num;
ber Rex in front of the dimple leading edge of 3940 to
110450.
The dimpled flat plate in the test section was sus;
pended upside down so that the flow structures could
be observed through the transparent (glass) floor with
the aid of an inclined mirror placed below the test
channel. To visualize the flow structures, five differ;
ent colors of dye were injected through five cylindrical
ports machined both upstream and inside the dimple.
A digital camcorder SONY;DCR VX2000 was used to
record the flow patterns within and downstream of
the dimple. A second camcorder was installed facing
one of the side walls so that observations could be
made from a side view perspective. All video images
were stored as digital (AVI) files to allow computer
screening at a reduced frame rate (slow motion) with
Adobe Premiere 6,5 software. In this way the flow
structures and patterns could be carefully observed,
analyzed, and characterized. The TSI’s two;dimen;
sional Laser Doppler Velocimeter was employed to
scan the boundary layer both in front and downstream
of each dimple.
Uncertainty Analysis
Using uncertainties of 1,2 mm for all dimensions
of the test section, and a 1,0 % uncertainty for prop;
erties of water at 297 K, the uncertainty in Reynolds
number was estimated to be within ± 2,4 %. Velocity
measurements were calibrated to within ± 1,8 %
using a video camera to record the time for a volume
of dye to go the length of the test section (video cam;
era frame rate is 29,97 frames per second). The fre;
quency of the bulk flow oscillations was determined
by counting the number of fluctuations shed by the
dimple during a 15 sec interval. The uncertainty in
frequency was estimated to be ± 10,6 %, which con;
tributed to an uncertainty in the Strouhal number of
± 10,9 %. This occurred at the highest velocity, where
the dye is diffused quickly making the fluctuations
difficult to count even at a reduced video frame rate.
At lower freestream velocities, both the frequency of
fluctuations and the Strouhal number were more pre;
cise (as low as ± 3,66% and ± 4,35%, respectively).
8 ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Figure 1. Schematic of the U.S. Air Force Academy Water Tunnel (a) and test section view (b).
1 – test channel. 2 – test section. 3 – inlet nozzle. 4 – axial flow pump. 5 – inclined floor mirror.
6 – digital camcorder (side observations). 7 – digital camcorder (top observations).
Ta b l e 1 . Dimple parameters and test cases
Finally, LDV measurements were estimated to be
± 3,5 %. The uncertainty in the extent of the separa;
tion zone inside the dimple is estimated to be within
± 7,8 % of the dimple diameter. All uncertainty esti;
mates are based upon the methods of Coleman and
Steele [23].
RESULTS AND DISCUSSIONS
Smooth flat plate
Before the dimples were machined into the plate,
preliminary measurements were made over the
smooth flat plate to characterize the primary flow
parameters. The LDV system was employed to meas;
ure velocity profiles at locations of 63 mm and
239 mm downstream of the flat plate leading edge at
potential dimple locations. The flow velocity in front
of the test section was 0,099 m/s and 0,49 m/s giving
the Reynolds numbers ReD 4500 and 22240. The fol;
lowing primary conclusions have been drawn after the
experimental data processing:
The freestream velocity over the flat plate
exceeded the inlet area;averaged velocity obtained by
the volumetric flow meter by less than 3 %.
At the lowest speed conditions the flow from
x=0 to x=239 mm was slightly decelerating, while at
the highest speed it was slightly accelerating from
x = 0 to 150 mm. However, in both cases the
freestream flow gradient factor f1 was far from the
flow separation conditions.
The pre;dimple boundary layer thickness data
is given in Table 2. For the distance of x = 63 mm the
difference between the measurements and calcula;
tions was within ± 14 %. At x = 239 mm the measured
results are below the predictions by 26 %. The shape
factor ratio H/H00 is equal to 1 ± 0,1 , where H00 is
the value associated with the Blasius solution.
The primary conclusion is that between
U∞ = 0,099 m/s and 0,49 m/s the average flow
parameters are fairly close to calculations obtained
from the Blasius solution within the range of experi;
mental uncertainty. However, the elliptically shaped
leading edge provides small flow “distortions” up to
the distance of x = 239 mm.
Pre-dimple flow parameters
Before the main experimental program, LDV
measurements were performed in front of the cylin;
drical dimple (x = xD) to identify the pre;dimple flow
parameters. The flow fields were scanned upstream
of the dimple front edge both on the dimple center;
line and in the spanwise direction 0,25 D and 0,50 D
off the centerline. Comparisons with the Blasius
solution (Table 3) revealed some differences between
measured and predicted values to be within ± 20 %.
As concluded, it is due to effect of the elliptical lead;
ing edge generating the local gradient flow.
At xD/D=0,66 upstream of the dimple and over
the centerline (Fig. 2a) the axial velocity profile cor;
responds to the typical shear flow, however small
reductions in the velocity profile can be seen above
the boundary layer edge. Apparently, it is due to the
convex curvature effect of the leading edge area. At
the same upstream location but z = 0,25D off the
centerline in the span wise direction (Fig. 2b), the
effect of the in;dimple flow separation zone,
unsteadiness, is present and the velocity profile expe;
riences significant fluctuations. The average velocity
profile, presented in Fig. 2b shows the “distortion
zone” thickness is around 1 mm (y/h ≈ 0,2). Further
from the dimple centerline (z = 0,5 D), the velocity
profile is close to the shear flow shape as given in
Fig. 2a. At xD/D = 4,04 along the centerline, the flow
is the “pure” shear flow, however at z = 0,25 D offset
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 9
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Ta b l e 2 . Boundary layer thickness data (flat plate) Ta b l e 3 . Pre;dimple boundary layer thickness
location, the velocity “irregularities” occur up to
y ≈ 2 mm (y/h ≈ 0,4). The shape factor H00 in front of
the dimple varies from around 2,20 at xD/D = 0,66 to
2,3…2,6 at xD/D = 4,04. The lower H00 magnitude at
xD/D = 0,66 can be explained by the convex curva;
ture effect of the elliptical leading edge area. The con;
clusion is that a laminar flow pattern occurs in front
of the dimple (centerline) at all flow regimes studied.
SINGLE CYLINDRICAL DIMPLE
Flow pattern (x/D=1,23)
Details of the flow patterns obtained from visual;
izations have been considered in depth in [14].
Fluctuations of the centerline streamlines and 0,25 D
offset streamlines become clear starting at ReD = 3200
accompanied with periodic bulk flow fluctuations
over the dimple axis. The region of in;dimple separat;
ed flow formed at ReD = 3200 and grew rapidly up to
ReD ≈ 8000, where the length of the separation zone
is around 0,45 D. The twin vortex appears at
ReD ≈ 4100 and grows to ReD = 9300, where the
maximum bulk flow oscillations were found. At
ReD = 9300 the extent of the separation zone
(0,45 D) is identical at both the centerline and at the
0,25 D offset. For ReD >6600 both 0,50 D offset
streamlines were drawn into the dimple space. The
rate of the twin vortex rotation increased with
Reynolds number. At ReD = 15100 the legs of the
twin vortex changed the sign of their rotation and cre;
ated a new vortex pair configuration with diverging
flow at the separation line. The extent of the separa;
tion zone grew to 0,73 D at ReD = 23450.
Flow pattern (x/D=4,70)
Measurements further downstream indicate that
an increase in the boundary layer thickness greatly
influences the flow pattern inside and downstream of
a dimple. Starting at ReD = 3200 the flow structure
becomes unsteady and alternates. The small size and
weakly fluctuating separation bubble was formed
behind the downstream dimple rim transforming
periodically into the wide wake flow pattern down;
stream of the dimple. At ReD > 8,000 the flow contin;
ued to alternate however it demonstrated an asym;
metric wake pattern. As expected, this is the
beginning of the turbulent flow formation inside the
dimple. Starting at ReD = 12200 the separated flow
forming inside the dimple accompanied the symmet;
rical wake downstream of the dimple. The separation
zone grows monotonically up to ReD = 23500, where
the separation zone extent is around 0,45 D. This is
however 70 % smaller than that for the dimple at
x/D = 1,23 and the same ReD number. Inside the
non;separated zone the flow streamlines are very
irregular. Starting at ReD = 18000 the weak twin vor;
tex type flow forms inside the dimple and grows slow;
ly up to ReD =23500.
The periodic and stable bulk flow fluctuations
downstream of the dimple began at ReD > 10000.
These fluctuations are considerably lower than that
observed for the cylindrical dimple at x/D=1,23. At
10 ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Figure 2. Average velocity in front of the cylindrical dimple (xD/D=0,66).
a: Dimple centerline. U∞∞ = 0,115 m/s, ReD=5220. b: 0,25 D spanwise offset. U∞∞ = 0,36 m/s, ReD = 16240.
ReD > 16500 the bulk fluctuations for both locations
(x/D = 1,23 and x/D = 4,7) are actually the same
which indicates that the pre;dimple boundary layer
thickness had little effect.
Flow fields downstream of the dimple
All measurements were performed over the centerline
downstream of the dimple. The inlet area;averaged flow
speed U∞varied from 0,115 m/s to 0,36 m/s giving the
ReD number range of 5220 to 16240. The LDV scanning
of the boundary layer was performed at the non;dimen;
sional distance of x*/D = 0; 0,50; 1,0; 2,0, and 3,0
downstream of the rear dimple rim. The following con;
clusions have been drawn from the measurements.
x/D=1,23. At the low flow speed a small area
of reduced speed (1 mm thick) arose immediately
after of the dimple. The 1 mm thick “kink” is not a
flow separation yet, but demonstrates the interaction
of “free” flow over a dimple and “back step” of the
rear dimple rim. At x*/D=0,5 and x*/D=2,0 the
velocity profile near the wall was close to the linear
law indicating the laminar flow pattern. At the high;
est speed a turbulent flow pattern arose immediately
downstream of the dimple which was maintained fur;
ther downstream. No flow separation was found over
the entire plate surface downstream of the dimple.
Therefore, at x*/D=1,23 the laminar;turbulent flow
transition occurs between ReD =5220 and 9430,
where the δ0av/h magnitude is 0,39 as follows from
Table 3. Here δ0avis the average boundary layer thick;
ness δ0 between ReD = 5220 and 9430.
x/D=4,70. At the low and middle flow speeds
a weak separation zone arose at x*=0, however at
x*/D>0,5 the laminar flow existed over the remainder
of the flat plate. At the highest flow speed a separation
zone begins at x*= 0 followed by a turbulent flow pat;
tern at x*/D>0,5. In this case, the transition to turbu;
lent flow occurs between ReD = 9430 and 16240 with
δ0av/h =0,98. Thus, the increase in the pre;dimple
boundary layer thickness increased Reynolds number
ReD where the laminar;turbulent flow transition
finally took place.
Conclusions yielded from this data are consistent
with the measured shape factor distributions present;
ed in Fig. 3. As a first approach, one may conclude
that for δ0av/h=0,39 transition to the turbulent flow
occurs at ReD ≈ 7235 (average value between two
“borders”), while for δ0av/h = 0,98 this occurs at
ReD ≈ 12835.
The flow that reaches the edge of a cylindrical
dimple sees a more abrupt drop off than for the flow
approaching a spherical indentation back rim. For the
flow along the dimple centerline, it is much more like
flow over a backward facing step. For the spherical
dimple, the rim of which is ‘smoother”, the laminar;
turbulent flow transition may occur at greater ReD
numbers then found for the cylindrical dimple.
SINGLE SPHERICAL DIMPLE
Flow pattern (x/D=1,23)
The flow patterns have been discussed in detail in
[14]. At low velocities (ReD = 3300…4200) all stream;
lines over the dimple were quite parallel and only
small fluctuations at (1,4 to 1,8 Hz) were observed
along the center streamline. These fluctuations were
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 11
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Figure 3. Shape factor H in front and downstream of cylindrical dimple.
a: x/D = 1,23. b: x/D = 4,70. 1 – ReD = 5220. 2 – ReD = 9430. 3 – ReD = 16240.
confined to a small zone near the downstream edge of
the dimple. As ReD was increased to 5,200, a separa;
tion zone began to form inside the dimple along the
downstream edge. At ReD > 6700 there was a slow and
periodically alternating clockwise and counter;clock;
wise bulk flow rotation inside the dimple with an
accompanying periodic migration of the separation
zone between the dimple centerline and the stream;
line offset from the centerline by 0,5 D. These rota;
tional fluctuations ceased at ReD = 12200 at which
point the separation zone became symmetrical with
respect to the dimple centerline. At ReD = 7900, a
weak twin vortex appeared inside the non;separated
zone inside the dimple. Thus, between ReD = 12200
and ReD = 21000, the flow inside the dimple includ;
ed both a twin vortex and a region of separation.
Finally, as ReD was increased to 23450, the separation
zone inside a dimple became very large, which led to
the elimination of the twin vortex structure. Only
chaotic streamlines could be seen within the non;sep;
arated zone near the upstream edge of the dimple.
The maximum frequency of bulk flow fluctuations
(f = 13,4 Hz) was found at ReD = 17900.
Flow pattern (x/D=4,70)
At low velocities and up to ReD = 10500 the flow
downstream of the dimple was of the “strip type”
transforming into asymmetrical wake flow at
ReD = 11400. An asymmetrical wake with a small
separation bubble existed until ReD=16900, e.g.
much longer than for the single spherical dimple
located at x/D=1,23 (lower δ0/h value). The fully
developed symmetrical flow after the dimple formed
only after ReD >17000. However, the length of the in;
dimple separation zone was much smaller than for the
dimple located at x/D=1,23. The maximum separa;
tion zone length was 0,35 D which was roughly half
the size of the zone for the dimple at x/D=1,23.
The bulk flow fluctuations downstream of the
spherical dimple became visible and regular only
above ReD ≈ 9000. Above this point the flow fluctua;
tions grew very rapidly and reached the maximum
Strouhal number at ReD ≈17000. This occurred while
there were the asymmetrical structures downstream of
the dimple. As a whole, in the Reynolds number
range of 10000 to 17000, the Strouhal number is of
40 % to 50 % lower of that for the dimple located at
x/D =1,23. Over ReD ≈ 24000, there is no effect of the
boundary layer thickness on the downstream bulk
flow fluctuations and the Strouhal numbers are virtu;
ally identical for both spherical dimples located at
x/D=1,23 and x/D=4,70 at this elevated ReD.
IN�DIMPLE SEPARATION ZONE EXTENT
The average length of the separated region L inside
the dimple was measured along the dimple centerline.
This length is the distance between the beginning of
the separated region and the downstream rim of the
dimple. The data taken from a few “frozen” video
images for the same Reynolds number was averaged
and presented in Fig. 4 as the non;dimensional length
L/D of the separated region plotted versus ReD num;
ber. At x/D =1,23 (low δ0/h value) for the cylindrical
dimple the flow separation began at ReD ≈ 3500,
while for the spherical dimple it originated at
12 ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Figure 4. Extent of the in�dimple separation zone over centerline: cylindrical (a) and spherical (b) dimple.
1 – x/D = 1,23. 2 – x/D = 4,70.
ReD ≈ 5200. In both cases the extent of the separation
zone increased monotonically as ReD increased, but
more appreciably between ReD = 5500 and 10000.
For the cylindrical dimple the length of the separated
zone was slightly greater than that of the spherical
dimple. Increase in the boundary layer thickness
(x/D = 4,7) reduced the separation zone more appre;
ciably for the spherical dimple. Also, the growth of
δ0/h delayed the formation of the separation zone to
higher Reynolds numbers.
BULK FLOW FLUCTUATIONS
Preliminary experiments documented in [14] have
identified suitable locations for the video camcorder so
that the bulk flow oscillations could be clearly observed
and recorded. As reported, the experimental data taken
from three independent test set;ups (top view: dye
injection in front of, and inside a dimple; side view)
yielded about the same value of Strouhal numbers
across a wide range of Reynolds numbers. All three
were used in subsequent measurements as a check for
consistency. Figure 5 is a plot of the local Strouhal
number versus the Reynolds number ReD for different
dimple locations. This correlation determines the bulk
flow oscillations downstream of the dimple.
For all cases, the Strouhal number curve reaches a
maximum value at a certain Reynolds number and then
drops off at higher ReD. The lower the pre;dimple
boundary layer thickness δ0/h, the higher the Strouhal
number. The cylindrical dimple at x/D=1,23 and
ReD < 12000 creates higher bulk flow oscillations than
the corresponding spherical dimple. At x/D=4,7 the
spherical dimple data exceeds cylindrical dimple results.
As a whole increases in the boundary layer thickness in
front of a dimple reduces the bulk flow oscillations.
Moreover, the Strouhal number maximum relates to the
greater Reynolds numbers for cylindrical dimples and to
the lower Reynolds numbers for the spherical dimples.
No effect from the boundary layer thickness was appar;
ent for the cylindrical dimples at ReD > 16500 and for
the spherical dimple at ReD > 24000.
Comparison of Figs 4 and 5 reveals that the spher;
ical dimple generates fluctuations even when there is
no separation zone. However, these fluctuations are
very small and located only in the narrow area next to
the axis. For the cylindrical dimple, the beginning of
the separation zone roughly coincides with consider;
able growth of bulk flow oscillations.
The rapid growth of Strouhal number occurs
immediately after the separation zone appears and
develops. In turn, the present study has shown the
separation zone extent is a function of the dimple
shape (spherical; cylindrical) and pre;dimple bound;
ary layer thickness δ0/h.
It seems the latter determines the ratio of a flow
mass situated in front of and inside a dimple. At low
δ0/h, this ratio is too small to prevent the flow separa;
tion and fluctuations inside the dimple, however at
higher δ0/h the higher mass of external flow “sup;
presses” the bulk flow oscillations.
CONCLUSIONS
1. The flow pattern inside of and downstream of
spherical and cylindrical dimples is inherently a
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 13
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Figure 5. Bulk flow oscillations beyond cylindrical (a) and spherical (b) dimple.
1 – x/D = 1,23. 2 – x/D = 4,70.
three;dimensional and unsteady flow with down;
stream bulk flow fluctuations. An increase in the rela;
tive boundary layer thickness (x/D growth) leads to
the onset of the specific flow patterns.
2. The dimple influences upstream flow parame;
ters, mostly appreciably at 0,25D offset of the dimple
centerline in the spanwise direction. These unsteady
distortions in the velocity profile are due to the influ;
ence of the in;dimple separated flow which is propa;
gated upstream.
3. An increase in the pre;dimple boundary layer
thickness reduces the extent of the in;dimple separa;
tion zone and the intensity of bulk flow fluctuations.
The rate of bulk flow fluctuations is in sync with in;
dimple separation zone growth.
4. No effects from the boundary layer thickness
were found for the cylindrical and spherical dimples
at ReD>16500 and ReD>24000 respectively.
5. The bulk flow oscillations “activate” the lami;
nar;turbulent flow transition, the lower the relative
boundary layer thickness, lower critical Reynolds
number.
6. The next target is studying of one and two
spanwise row of dimples relevant to flow separation
control technique and heat transfer augmentation.
ACKNOWLEDGMENTS
This research was performed while visit of Prof. A.
Khalatov to the Aeronautics Laboratory of the U.S.
Air Force Academy in Colorado Springs. The partial
support of CRDF Grant # UE2;552;KV;02,
Collaborative NATO Linkage Grant #
PST.CLG.979702 (2003;2005) is also acknowledged.
REFERENCES
1. Lake J.P., King P.I., Rivir R.B. Low Reynolds
Number Loss Reduction on Turbine Blades with
Dimples and V;Grooves // AIAA Paper 2000;738.
2000.
2. Rouser K. Use of Dimples to Suppress
Boundary Layer Separation on a Low Pressure
Turbine Blade. – M.S. Thesis, Air Force Institute of
Technology, 2002, WPAFB, Ohio, USA.
3. Кикнадзе Г.И., Гачечиладзе И.А., Олейни�
ков В.Г., Алексеев В.В. Механизмы смерчевой ин;
тенсификации тепломассообмена // Труды 1;ой
Российской национальной конференции по теп;
ломассобмену. – Москва: Изд. МЭИ. – 1994. –
Т. 8. – С. 97 – 106.
4. Афанасьев В.Н., Чудновский Я.П. Экспери;
ментальное исследование структуры течения в
одиночной впадине // Москва: Вестник МГТУ. –
Сер. Машиностроение. – 1993. – №4. – С.85 – 95.
5. Щукин В.К., Козлов А.П., Чудновский Я.П.,
Агачев Р.С. Интенсификация теплообмена сфе;
рическими лунками // Доклады РАН. – Сер.
Энергетика. – 1998. – No 3. – С.47 – 64.
6. Нагога Г.П. Эффективные способы охлаж;
дения лопаток высокотемпературных газовых
турбин. – М: Изд. МАИ, 1996. – 99с.
7. Гачечиладзе И.А. Теплообмен при самоор;
ганизации вихревых структур. – В книге: “Тепло;
и массобмен. Конвективный теплообмен (Про;
блемные доклады)”. – Mинск: Изд. ИTMO AН
BССР. – 1988. С.83 – 125.
8. Терехов В.И., Калинина С.В., Мшвидобадзе Ю.М.
Теплоотдача от каверны сферической формы,
расположенной на стенке прямоугольного канала
// Теплофизика высоких температур. – 1994. –
Т. 32. – No 2. – С.249 – 254.
9. Терехов В.И., Калинина С.В., Мшвидобадзе Ю.М.
Теплоотдача от сферической лунки, расположен;
ной в следе другой лунки // Теплофизика и аэро;
механика. – Сибирское Отделение РАН. – 2001. –
Т. 8. – No 2. – С.237 – 242.
10. Езерский А.Б., Шехов В.Г. Тепловая визуа;
лизация потока около единичной лунки // Изве;
стия РАН. – Механика жидкости и газа. – 1989. –
No 6. – С.161 – 164.
11. Боровой В.А., Яковлев Л.В. Теплообмен в
единичном углублении при сверхзвуковом обте;
кании // Известия РАН. – Механика жидкости и
газа. – 1993. – No 5. – С.48 – 52.
12. Кесарев В.С., Козлов А.П. Структура тече;
ния и теплообмен при обтекании полусферическо;
го углубления турбулизированным потоком воздуха
// Москва: Вестник МГТУ. – Сер. Машинострое;
ние. – Москва. – 1993. – No1. – С. 106–115.
13. Snedeker R.S., Donaldson C.P. Observation of
a Bi;stable Flow in a Hemispherical Cavity // AIAA
Journal. – Vol. 4. – No 4. – 1966.
14. Khalatov A.A., Byerley A., Seong�Ki Min,
Ochoa D. Flow Characteristics Within and
14 ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
Downstream of Spherical and Cylindrical Dimple on
a Flat Plate at Low Reynolds Numbers // ASME
Paper No GT2004;53656. 2004.
15. Khalatov A.A., Byerley A., Seong�Ki Min &
Vincent R. Application of Advanced Techniques to Study
Fluid Flow and Heat Transfer Within and Downstream
of a Single Dimple // Материалы 5;го Международ;
ного форума по тепло; и массообмену. Минск:
Изд;во ИТМО АНБ. – 2004. – С. 1–20 (англ.).
16. Wighart K. Erhohung des Turbulenten Reib;
ungswidestandes Durch Oberflachen;Storungen //
Forschungshefte fur Schiffstechnikю – 1953. – No 1. –
pp. 65– 81.
17. Hiwada M., Kawamura T., Mbuch J., &
Kumada M. Some Characteristics of Flow Pattern
and Heat Transfer Past a Cylindrical Cavity //
Bulletin of JSME. – 1983. – Vol. 26. – No 220. – pp.
1744 –1758.
18. Kovalenko G.V., Khalatov A.A. Fluid Flow and
Heat Transfer Features at a Cross;Flow of Dimpled
Tubes in a Confined Space // ASME Paper No
GT2003;38155. 2003.
19. Isaev S.A., Leont’ev A.I., Zhdanov V.I.
Simulation of Tornado;Like Heat Transfer at Flow
Passing a Relief with Dimples // Heat Transfer;2002.
– Proceedings of 12th International Heat Transfer
Conference. Grenoble, France. – pp. 735–738.
20. Ligrani P.M., Oliveira M.M., Blaskovich T.
Comparison of Heat Augmentation Techniques //
AIAA Journal. – 2003. – Vol. 41. – No 3. –
pp. 337–362.
21. Ligrani P.M., Harrison J.L., Mahmood G.I.,
Hill M.L. Flow Structure due to Dimple Depression
on a Channel Surface // Physics of Fluids. – 2001. –
Vol.13. – No11. – pp. 3442–3451.
22. Burgess N.K., Ligrani P.M. Effects of Dimple
Depth on Nusselt Numbers and Friction Factors for
Internal Cooling in a Channel // ASME Paper No
GT2004;54232. 2004.
23. Coleman H., Steele G. Experimentation and
Uncertainty Analysis for Engineers. ;John Wiley &
Sons. New York, NY. 2d Edition. – 1999. – 275p.
Получено 13.07.2006 г.
ISSN 0204�3602. Пром. теплотехника, 2006, т. 28, № 5 15
ТЕПЛО+ И МАССООБМЕННЫЕ ПРОЦЕССЫ
УДК 629.12.03
БАСОК Б.И., РЫЖКОВ С.С.
Институт технической теплофизики НАН Украины
ИССЛЕДОВАНИЕ ВЛИЯНИЯ НЕИЗОТЕРМИЧНОСТИ
ПЛОСКОГО КАНАЛА НА ХАРАКТЕРИСТИКИ
ДИСПЕРСНОГО ДВУХФАЗНОГО ПОТОКА
Виконано розрахунок основних теп+
лофізичних та гідродинамічних характе+
ристик дисперсного двофазного сере+
довища для гладкого каналу в
тривимірній постановці. Встановлено
відсутність впливу перепаду температур
до 80 oС на розподіл швидкості, кінетич+
ної енергії турбулентності і статичного
тиску та встановлено вплив на концент+
рацію дисперсної фази двофазного се+
редовища в каналі. Основне зниження
концентрації дисперсної фази двофаз+
ного середовища (більше 95 %) відбу+
вається за рахунок осадження часток на
верхній і нижній стінках каналу. Осад+
Выполнен расчет основных тепло+
физических и гидродинамических ха+
рактеристик дисперсной двухфазной
среды для гладкого канала в трехмер+
ной постановке. Установлено отсутст+
вие влияния перепада температур до
80 oC на распределение скорости, кине+
тической энергии турбулентности и ста+
тического давления, и установлено вли+
яние на концентрацию дисперсной
фазы двухфазной среды в канале. Ос+
новное снижение концентрации дис+
персной фазы двухфазной среды (бо+
лее 95 %) происходит за счет
осаждения частиц на верхней и нижней
Research of main thermalphysic and
hydrodynamic characteristics of disperse
dysphasic environment for the flat 3+D
channel has been executed. Temperature
drop –up to 80 oC do not influence on
velocity distribution, Turbulent kinetic
energy, static pressure but influence on
concentration of disperse dysphasic
environment in the channel. Main con+
centration decrease of disperse dyspha+
sic environment (up to 95%) happens
with the help of particles sedimentation
on the up and down channel walls.
Sedimentation on the back wall could not
be taken into consideration and it is pos+
|
| id | nasplib_isofts_kiev_ua-123456789-61435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0204-3602 |
| language | English |
| last_indexed | 2025-11-24T07:56:17Z |
| publishDate | 2006 |
| publisher | Інститут технічної теплофізики НАН України |
| record_format | dspace |
| spelling | Khalatov, A. Byerley, A. 2014-05-05T14:12:46Z 2014-05-05T14:12:46Z 2006 Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple / A. Khalatov, A. Byerley // Промышленная теплотехника. — 2006. — Т. 28, № 5. — С. 5-15. — Бібліогр.: 23 назв. — англ. 0204-3602 https://nasplib.isofts.kiev.ua/handle/123456789/61435 532.516:536.24.01 This study is to investigate the details of the average and unsteady flow structures in front, inside and downstream of the shallow spherical and cylindrical dimple placed on a flat plate at the different distances with different pre-dimple boundary layer thicknesses. A comparison of both spherical and cylindrical dimple geometric configurations was made to assess their relative benefits. Досліджено особливості осередненої та нестаціонарної структури потоку перед, всередині і за дрібними заглибленнями циліндричної та сферичної форми, які зроблені на плоскій пластині на різних відстанях від входу, що забезпечує різну товщину пограничного шару набігаючого потоку. Порівняно характеристики заглиблень циліндричної та сферичної форми. Исследованы особенности осредненной и нестационарной структуры потока перед, внутри и за “мелким” углублением цилиндрической и сферической формы, выполненным на плоской пластине на различных расстояниях от входа, что обеспечивает различную толщину пограничного слоя набегающего потока. Сделано сравнение характеристик углублений цилиндрической и сферической формы. This research was performed while visit of Prof. A. Khalatov to the Aeronautics Laboratory of the U.S. Air Force Academy in Colorado Springs. The partial support of CRDF Grant # UE2-552-KV-02, Collaborative NATO Linkage Grant # PST.CLG.979702 (2003-2005) is also acknowledged. en Інститут технічної теплофізики НАН України Промышленная теплотехника Тепло- и массообменные процессы Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple Влияние толщины пограничного слоя на характеристики потока внутри и за одиночным мелким углублением Article published earlier |
| spellingShingle | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple Khalatov, A. Byerley, A. Тепло- и массообменные процессы |
| title | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| title_alt | Влияние толщины пограничного слоя на характеристики потока внутри и за одиночным мелким углублением |
| title_full | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| title_fullStr | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| title_full_unstemmed | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| title_short | Effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| title_sort | effect of pre-dimple boundary layer thickness on flow characteristics within and downstream of a single shallow dimple |
| topic | Тепло- и массообменные процессы |
| topic_facet | Тепло- и массообменные процессы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/61435 |
| work_keys_str_mv | AT khalatova effectofpredimpleboundarylayerthicknessonflowcharacteristicswithinanddownstreamofasingleshallowdimple AT byerleya effectofpredimpleboundarylayerthicknessonflowcharacteristicswithinanddownstreamofasingleshallowdimple AT khalatova vliânietolŝinypograničnogosloânaharakteristikipotokavnutriizaodinočnymmelkimuglubleniem AT byerleya vliânietolŝinypograničnogosloânaharakteristikipotokavnutriizaodinočnymmelkimuglubleniem |