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Flow Characteristics and Structures of Inclined Jets in a Crossstream over a Concave Wall

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Title: Flow Characteristics and Structures of Inclined Jets in a Crossstream over a Concave Wall


1
?????????????????????Flow Characteristics and
Structures of Inclined Jets in a Cross-stream
over a Concave Wall
  • ???
  • I-Chien Lee
  • ??????? ??
  • Advisor Ping-Hei Chen, Ph.D.
  • December 17, 2007

2
Outline
  • Motivation Objective
  • Introduction
  • Experimental apparatus set-up
  • Operation conditions and measurement uncertainty
  • Results and discussions
  • A jet in a cross-stream
  • A row of jets in a cross-stream
  • Conclusions and Prospects

3
Motivation Objective Inclined Jets in a
Cross-stream over a Concave Wall
  • Motivation
  • Rarely experimental studies discussed a 3D
    velocity flowfield and especially the
    interaction between the jet and cross-stream. In
    a viewpoint of film cooling, the domination of
    jet flow or cross-stream in the flowfield will
    affect the cooling efficiency.
  • Objective
  • This study is to experimentally construct a 3D
    velocity flowfield of inclined jets in a
    cross-stream over a concave surface and to
    classify which flow is dominant.

4
Literature review Jets ejected to a cross-stream
  • Previous studies show that jet lift-off, high
    turbulence intensity in the shear layer, and
    counter-rotating vortex pairs are important
    features of film cooling.
  • Various geometric and fluid dynamics parameters
    affect film cooling performance.
  • Geometric factors include hole spacing, hole
    length, hole shape, inclination angle, compound
    angle, surface curvature, and smoothnessetc.
  • Fluid dynamics parameters include velocity ratio,
    momentum flux ratio, density ratio, free-stream
    turbulence intensity, and cross-stream pressure
    gradientetc.

5
Basic structuresA jet ejected normal to a
cross-stream
  • Counter-rotating vortex pair (CVP)
  • embedded in the jet
  • a large scale mixing and to cause an enhancement
    of cross-stream entrainment into the jet.
  • the dominant flow structure
  • Wake vortices
  • beneath the downstream of the jet near the wall
    surface
  • Ring vortices
  • occurring at the windward side of the jet
  • Horseshoe vortices
  • occurring upstream of the jet

Sourced from Fric and Roshko9
6
Experimental apparatus1. The experimental set-up
  • 1. Inlet section (D420 300mm)
  • 2. Blower (1 Hp 0.75KW, D420mm, centrifugal
    fan)
  • 3. Honeycomb
  • 4. Diffuser (D420 to 450 450mm, L450mm)
  • 5. Screens (three wire meshes)
  • 6. Contraction (450 450 to 150 150 mm,
    L400mm)
  • 7. Straight duct (150150270 mm)
  • 8. Curved duct (150 150 mm 135)
  • 9 Outlet straight duct (150 150 100 mm)
  • 10. Jet supply section and seeding generator
  • 11. Buffer tank
  • 12. Valves
  • 13. Air flow meter
  • 14. Pressure regulators
  • 15. Air storage tanks (0.66 m3 2)
  • 16. Air compressors (5 Hp 2)

7
Experimental apparatus2. Injection holes
geometry
  • The streamwise inclined angle of 35 o with a
    forward expanded angle of 8 o.
  • Holes position located at an angle 34 from the
    onset of concave curvature
  • The length-to-diameter ratio of injected holes
    2.2.

8
Experimental apparatus3. The PIV set-up
  • Double pulsed Laser
  • A Q-switched NdYAG pulsed laser with a
    wavelength of 532 nm
  • A maximum output energy of 15 mJ/pulse.
  • PIV processor
  • A Dantec FlowMap 2500 processor with a buffer
    memory of 8 GB
  • CCD camera
  • A Kodak ES1.0 CCD camera with a resolution of
    10081016 pixels and a pitch of 99 µm pixel.
  • A Nikon AF Micro 60 f/2.8D lens and a 532 nm
    filter lens.
  • Workstation
  • P III dual CPU 1 GHz
  • Traversing system
  • Dantec 41T50, 80 pulses/mm

Double pulsed Laser
Light guiding arm
Laser sheet optics
PIV Processor
CCD Camera
Workstation
Traversing system
9
Experimental apparatus4. The Hot-wire sensor
set-up
  • A hot-wire anemometer (Dantec, StreamLine 90C10)
  • A duel-sensor hot-wire probe (Dantec, 55P63) and
  • A boundary layer hot-wire probe (Dantec, 55P15).
  • A manual traversing stage with a minimum
    increment of 0.1 mm

10
PIV operating conditionsParameters set-up
  • Based on the FFT/Correlation theory of PIV, the
    following is processed
  • To optimize the seeding density
  • To set ?t1 µs (the flow field effectively does
    not move) and display a quality indicator () of
    the signal-to-noise ratio (S/N) at an incoming
    zero displacement map.
  • To increase the seeding density so that the
    quality indicator less than 5 at a threshold,
    S/N1.15 at the worst condition.
  • To increase ?t gradually until a little
    deterioration is happened yet. (The maxi.
    displacement of particles ? ¼ of the
    interrogation area.)
  • The use of Gaussian window functions eliminates
    cyclic noise due to correlation by FFT
  • The use of filters reduces noise and to optimize
    the effectiveness of sub-pixel interpolation

11
PIV operating conditionsParameters conditions
  • The velocity vectors are obtained by calculating
    the cross-correlation coefficient between two
    consecutive recorded particle images.
  • A single jet
  • Time between pulses range between 10 and 32 µs
  • 1616 pixel interrogation windows with a 50
    overlap grid.
  • A row of jets
  • Time between pulses 32 µs
  • 3232 pixel interrogation windows with a 50
    overlap grid.
  • The time-averaged velocity vectors are acquired
    with a sampling rate of 15 Hz and are averaged
    over 600 instantaneous image pairs.

12
PIV operating conditionsTime-averaged velocity
and its rms
  • The values for SR and N depend primarily on the
    required data analysis (time-averaged or spectral
    analysis) and the acceptable level of
    uncertainty.
  • Time-averaged analysis such as time-averaged
    velocity and rms
  • Requires non-correlated samples, which can be
    achieved when the time between samples is at
    least two times larger than the integral time
    scale of the velocity fluctuations.
  • Estimate the following expected quantities in the
    flow
  • velocity U 12 m/s
  • turbulence intensity Tu 30 ,
  • integral time-scale T1 .0005 s
  • Select
  • the wanted uncertainty uncertainty u 3 ,
    in U0
  • confidence level 95 (Za/2 1.96)
  • Calculate the sampling rate SR
  • Calculate the number of samples N

13
Operating conditionsCross-stream
  • Potential velocity measured by a hot-wire
    anemometer, a total 200,000 data were acquired
    for each channel at a sampling rate of 10 kHz per
    channel.
  • The cross-stream reference point at 200 mm
    upstream starting from the onset of curved
    section.
  • The potential flow velocity keeps 12.0 m/s with
    T.I. 1.5 .
  • The Reynolds number is 5820 based on the diameter
    of injection holes.

14
Calibration and measured errors1. Calibration
of PIV
  • A grid target uses to calibrate the actual
    displacement.
  • The measured displacement error sources from
    scattered light passed a curved surface.

(DANTEC, 908X0321) Size of 75 mm by 95 mm with
an exact dot spacing of 10 mm
15
Calibration and measured errors 2. the drifting
of seeded particles
  • Measurement errors caused by tracer particles
    primarily arise from particle inertia and
    gravity.
  • 1. Particle inertia
  • Stokes numbers are defined as the ratio of
    particle response time based on Stokes drag to
    the flow time scale

Where
  • 2. Gravitational force
  • Particle sedimentation velocity Ug

16
Measurement uncertainty- Hot-wireError sources
of the hot-wire anemometry
  • The uncertainty of each individual velocity
    sample is determined by
  • The instrumentation, calibration equipment
  • Anemometer Drift, noise, repeatability and
    frequency response
  • Calibrator
  • Linearization (Conversion)
  • A/D board resolution
  • Experimental conditions.
  • Probe positioning
  • Temperature variations
  • Ambient pressure variations
  • Gas composition, humidity

17
Measurement uncertainty Hot-wireThe total
relative expanded uncertainty
Total relative expanded uncertainty
18
Measurement uncertainty- PIVComparisons of
velocity distributions
  • To use a hot-wire anemometer to check the
    time-averaged velocity measured by PIV.

(a) Ux/U0, (b) Uz/U0 Comparisons of velocity
distributions normal to the wall on the hole
central plane of Y/D0.0.
19
Measurement uncertainty- PIVConvergence of
time-averaged velocity
  • To take several independent data sets of
    instantaneous velocity vector fields by PIV

(a) Sampling no. (b) Sampling no. The
convergence of time-averaged at a point locating
at (X/D, Y/D, Z/D) (2.8, -0.63, 0.31) from 2700
captured images. .
20
Measurement uncertainty- PIVError sources of PIV
  • The total errors, Etotal, can express as the sum
    of a bias error, Ebias, and a random error,
    Erandom. ( Etotal Ebias Erandom )
  • The Ebias can arise from several sources
  • The particle image size
  • Size of the interrogation area
  • Local velocity gradients
  • Numbers of seeding particle within interrogation
  • Receiving optics, and post-processing
  • For the Erandom, a grid target used to calibrate
    the actual displacement and checked by the
    convergence of the time-averaged velocity.
  • Following the uncertainty calculated at a 95
    confidence level yields uncertainty in the
    time-averaged velocity measurements of 3 of
    reading based on averaging 600 images

21
Cross-stream in the curved duct slightly
accelerated above the concave surface
  • In this study, the cross-stream is slightly
    accelerated over the concave surface in measured
    region of X/D ranging from -0.5 to 7.0.
  • Schultz and Volino 35 stated that The measured
    boundary layer thickness, d, is
  • d The distance from the surface to the point at
    which the velocity is 0.995 of the potential flow
    velocity (Up) on the measured point.
  • In this study
  • d 6.1 mm at the onset of the curved section.
  • d 17.0 mm at the upstream leading edge of the
    ejected hole.

r
Potential flow region
U(r)
Boundary Layer region
The fitting line means the potential velocity
distribution in a potential flow region
22
A jet in a cross-streamTypical instantaneous
images of seeded particles
S/D 2.5 3.8 9.0
  • The jet lifts away the measured wall gradually as
    the value of blowing ratio, M, increases.
  • M0.5 the jet flow still keep close to the wall.
  • M1.0 the jet flow is close to the wall.
  • M1.5 and 2.0 jets lift away the wall.

(a) M0.5, (b) M1.0, (c) M1.5 (d) M2.0
23
A jet in a cross-streamTime-averaged particle
concentrations of the jet flow
S/D 2.5 3.8 7.0
  • All three figures of contours Cj0.9 show that
    the main areas of the jet flow have clear kidney
    shapes, caused by a counter-rotating vortex pair
    (Sivadas et al.39).
  • The jet at M1.0
  • S/D 2.5 lifts off.
  • S/D3.8 is pushed towards the wall.
  • S/D7.0 attaches to the wall
  • The moderate blowing ratio of M1.0 will give a
    well protection for the wall.

(a) M0.5, (b) M1.0, (c) M1.5
24
A jet in a cross-streamContours of dimensionless
velocity at M 1.0
(a) Streamwise velocity,Us/U0 (b) the defect
velocity of Us/U0 (c) The velocity defect of Us/U0
(d) Radial velocity,Ur/U0 (e) the defect
velocity of Ur/U0 (f) The velocity defect of Ur/U0
  • Us/U0 and Ud,s/U0 have similar distributions away
    from boundary lines.
  • Us/U0 ?Ud,s/U0 near the leeward side of the jet
    boundary.
  • the positive radial cross-stream provides a
    lift-off velocity to keep the jet away from the
    wall.

25
A jet in a cross-streamContours of dimensionless
turbulence intensity at M 1.0
(a) Turbulence Intensity, Tu (b) The defect
velocity of Tu
  • The high turbulence intensity mainly comes from
    the interaction between jet and cross-stream on
    the leeward side of jet flow.

26
A row of jets in a cross-streamTypical
instantaneous images of jet end view at M 1.0
s/D 2.0 3.8 5.0 10.0
  • Similar cross-section shapes at S/D2.0 give a
    good uniform flow distribution.
  • Jet development along downstream

S/D2.0 Jets have individual cross-section. S/D
3.8 Jets are unsteadily distorted and merged on
lower parts at the near wall region. S/D3.8 to
5.0 jets merges gradually on the bottom of
adjacent jets and upwardly spreads to the whole
jet. S/D5.0 to 10.0 a jet-film layer attached
to the wall.
27
A row of jets in a cross-streamTypical
instantaneous and time-averaged images of jet top
view at M 1.0
  • The Kelvin-Helmholtz Instability appears when the
    velocity difference across the interface between
    jet and cross-stream.
  • The time-averaged jet shapes gradually change
    from a kidney shapes near the hole exit to an
    oval shapes at Z/D 0.88.

(a) Z/D0.13, (b) Z/D0.31, (c)
Z/D0.63, (d)Z/D0.88
28
A row of jets in a cross-streamTime-averaged
concentrations of jet, Cj, and cross-stream, Cm,
at M 1.0
Z/D 0.13 0.31 0.63 0.88
  • Cj 0.95 Contours show clear kidney shapes
    above the exit of the injection hole.
  • Cm 0.8 A high concentration of cross-stream
    behind the injection hole downstream.
  • Z/D 0.88 The cross-stream passes through the
    jet flow.

(a) Seeding jet flow, Cj (b) Seeding
cross-stream, Cm
29
A row of jets in a cross-streamTime-averaged
velocities on the streamwise and transverse
direction
Z/D 0.13 0.31 0.63 0.88 1.13
  • In the streamwise direction
  • Jet has been bent by a cross-stream and then has
    main streamwise velocity at both transverse sides
    of a hole trailing edge on Z/D0.31 plane.
  • In the transverse direction
  • Jet flows on both sides of injection holes move
    towards the centerline of the hole downstream on
    Z/D0.13 plane.

(a) Streamwise time-averaged velocity, Ux/U0
(b) Transverse time-averaged velocity, UY/U0
30
A row of jets in a cross-streamTime-averaged
velocities on the vertical direction
Y/D 0.0 -0.25 -0.63 -0.75
  • Y/D 0.0 A local maximum region of UZ/U0 is
    produced by the impingement of opposite traverse
    flow motions towards the centerline of the
    injection hole.
  • Y/D -0.63 and -0.75 The negative values of
    UZ/U0 produce a the downwash of the jet flow.

31
A row of jets in a cross-streamReconstruction of
the 3D time-averaged velocity
  • The 2D time-averaged velocity fields were
    acquired on six horizontal XY planes, Z/D
    (0.13, 0.31, 0.63, 0.88, 1.13, and 1.38) and on
    six vertical XZ planes Y/D (0, -0.19, -0.25,
    -0.45, -0.63, and -0.75).
  • Two 2D velocity vectors on the intersection line
    were used to establish a 3D time-averaged
    velocity vector.

32
A row of jets in a cross-stream Cross-sectional
views of the YZ plane streamline distributions
(a) X/D2.0, (b) X/D3.0, (c) X/D4.0, (d)
X/D5.0
  • This maximum vorticity is mainly produced by the
    larger vertical velocity gradient ( ) in
    the transverse direction on the X/D2.0 plane.
  • A zero-velocity boundary line of UYZ/U0 exists to
    separate the jet and swirling flow on the X/D4.0
    plane.

33
A row of jets in a cross-stream Perspective
views of jet flow streamline distributions
(a) Y/D -0.025
  • A straight flow zone Near jet hole center
    plane, the jet flow moves almost straight
    downstream.

34
A row of jets in a cross-stream Perspective
views of jet flow streamline distributions
(b) Y/D -0.25
  • A swirling flow zone As the value of Y/D
    increases, jet flow swirling becomes more
    significant along the downstream.

(c) Y/D -0.30
35
A row of jets in a cross-stream Perspective
views of jet flow streamline distributions
(d) Y/D -0.375
  • A touch-down flow zone Near the transverse
    edge of the injection hole, the reattachment of
    jet flow is caused by blockage of the
    cross-stream.

(e) Y/D -0.45
36
A row of jets in a cross-stream The trace of jet
flow on the X/D7.0
  • Different transverse levels of the jet flow
    construct the scatter distributions on X/D7.0
    plane and form a kidney-shape profile referred to
    the transverse symmetry.
  • The jet flow near leading edge of the injection
    hole travels to the outside layer on X/D7.0
    plane and encloses it.
  • The jet flow near trailing edge of the injection
    hole travels to the inner layer on X/D7.0 plane.

mark u the position of a leading edge mark
d the position of a trailing edge
37
A row of jets in a cross-stream Temporal
evolution of a circular ring starting from the
exit of an injection hole above
  • The circular ring near trailing edge of the
    injection hole is tilted up.
  • The circular ring in the transverse direction is
    stretched by the transverse shear stress.

38
A row of jets in a cross-stream Temporal
evolution of a vortex ring near the exit of an
injection hole
  • The vortex lines are stretched in the transverse
    direction by the streamwise vorticity.
  • The line 7 shows that jets ejected from a row of
    five inclined holes merge downstream and form a
    jet layer scattered over the wall surface.

39
A row of jets in a cross-stream Perspective
views of cross-stream streamline distributions
(a) Z/D 0.15
  • The cross-stream speeds up, caused by the jet
    flow, above the injection hole.
  • The streamline cut-off on the end is caused by
    the mix between cross-stream and jet flow.

40
A row of jets in a cross-stream Perspective
views of cross-stream streamline distributions
(b) Z/D 0.4
  • As the streamlines starting elevation increase,
    streamlines seem to form a shell covering the jet
    flow above the injection hole.

(c) Z/D 0.6
41
A row of jets in a cross-stream Perspective
views of cross-stream streamline distributions
(d) Z/D 0.8
  • Above Z/D1.0, cross-stream is slightly affected
    by the jet flow.

(e) Z/D 1.0
42
Why the cross-stream has a high concentration
area behind the leeward side of the jet flow.
  • The jet flow dominates the mixing flow
  • The jet flow at the near-wall region accelerates
    the boundary layer velocity of the cross-stream
    passing between two adjacent jets, the jet flow
    should dominate the mix of jet flow and
    cross-stream.
  • The jet flow streamwise vortex inducing
  • The jet flow streamwise vortex causes the mix to
    flow towards the wall. Therefore, part of the
    mixing cross-stream is induced into the leeward
    side of the jet flow.
  • This movement creates a high cross-stream
    concentration behind the injection hole
    downstream.

43
Conclusions (1)
  • the flowfields of both an inclined jet and a row
    of five inclined jets ejected from a forward
    expanded hole into a cross-stream over a concave
    surface.
  • Following conclusions are drawn from the
    experimental results
  • An inclined jet though a forward expanded hole
    into cross-stream over a concave surface
  • Visualization shows that a single jet in a
    cross-stream flows along wall surface, lifts up
    and touches the wall surface again, and lifts
    farther from the wall surface at different
    blowing ratios of 0.5, 1.0, and more than 1.5
    respectively.
  • A cross-stream located on the downside of the
    ejected flow possesses a lift-off velocity at
    M1.0 to keep the ejected flow away from the wall.

44
Conclusions (2)
  • A row of five inclined jets though a forward
    expanded hole into cross-stream over a concave
    surface at M1.0.
  • Flow visualization shows that cross-section
    shapes develops along streamwise are
  • stable individual jets, unsteadily distorted and
    then gradually merged with adjacent jets, and a
    jet-film layer.
  • The jet ejected from an inclined jet possess a
    kidney-shaped cross-section and cannot be passed
    through by the cross-stream at the near hole
    exit. At an elevation of Z/D0.88, the
    cross-stream can pass through the main jet.
  • A counter-rotating secondary-flow vortex pair
    forms in the jet at locations between X/D2.0 and
    5.0 downstream.

45
Conclusions (3)
  • The ejected jet flow at transverse locations can
    be categorized into three flow zones
  • a straight flow zone.
  • a swirling flow zone.
  • a touch-down flow zone.
  • Jet trajectory and vortex line evolutions
    indicate that the main jet flow is bent at the
    windward side and dragged at the transverse
    sides.
  • The jet flow dominates the mix of jet flow and
    cross-stream at the near-wall region . The jet
    flow streamwise vortex induces the cross-stream
    into the leeward side of the jet flow. It causes
    that a high cross-stream concentration behind the
    injection hole downstream.

46
Future Prospects
  • Except for this work of studying jets ejected
    into a cross-stream, the following advanced
    researches should be worked.
  • The geometry effects of several film cooling
    parameters should be investigated, including the
    effects of concave curvature, hole cross-section
    geometry, injection angle, hole length, hole
    spacing and hole arrangement.
  • In addition, the fluid effects of several film
    cooling parameters also should be studied,
    including the effects of jet-to-cross-stream
    velocity ratio (more detailed variation),
    cross-stream turbulent intensity, and streamwise
    pressure gradient of cross-stream.
  • Due to the complexity of jets in a cross-stream,
    there is difficult to research this mixed flow
    using numerical or analytical techniques. This
    experimental study can provide a good assistance
    to establish the suitable models to approach the
    real flow structure.

47
Thanks for your attention !
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