Page 1 of 12
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`Samsung Exhibit 1023
`Samsung Electronics Co., Ltd. v. Daniel L. Flamm
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`T. LIU and .l. P. SULLIVAN
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`NOMENCLATURE
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`specific heat [J kg’ ' K E]
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`nonle diameter [m]
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`output voltage of anemometer [Volt]
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`E without flow [Volt]
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`voltage fluctuation [Volt]
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`natural frequency [Hz]
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`excitation frequency [H7]
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`local convective heat transfer
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`coeflicient [W in’ 3 K "]
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`nozzle-to-plate spacing [rn]
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`fluorescence intensity [J 5
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`thermal conductivity of air
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`[W m ' K ']
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`Nusselt number, /1D/k
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`stagnation-point Nusselt number
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`Prandtl number, pcpv,/k
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`local convective heat transfer rate
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`[W m’ 3]
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`convective heat transfer rate at
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`stagnation—point [W m 3]
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`heat flux from heated steel sheet
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`surface [W m ' 3]
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`local convective heat transter
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`fluctuation [W 111*]
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`radial coordinate [in]
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`correlation coefficient,
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`Q'(I+I. 0)u’(I-.1‘)/(Q'H’)
`Reynolds number, U.,D/v
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`temperature [°C]
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`reference temperature ["C]
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`temperature of heated steel sheet
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`surface [“C]
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`ambient temperature [ C]
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`temperature fluctuatio11[ C]
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`jet exit velocity [m s"]
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`streamwise velocity [in s
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`streamwise fluctuating velocity [m s
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`fluctuating velocity normal to wall
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`lm 8”]
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`streamwise cordinate in free jet [in]
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`coordinate normal to wall [in].
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`Greek symbols
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`-1,
`spatial amplification rate [in ']
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`factor of heat transfer enhancement.
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`Qt./L)/QU; = 0)—l
`kinematic viscosity [m3 s’ 1]
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`momentum thickness [In]
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`initial momentum thickness [In]
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`density of air [kg m"‘].
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`7]
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`heated steel sheet
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`1 aifflgw
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`painted side
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`CCD Camera
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`Fig.
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`(b)
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`1 Experimental set-up: (a) jet facility,
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`system,
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`(13) coordinate
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`maximum deformation of the sheet due to low speed
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`jet impingement is less than 0.1 mm. Note that the jet
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`impingement cooling could cause spatial variation of
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`the sheet resistivity and consequently lead to non—
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`uniform heating. The measurements of the spatial
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`variations of the sheet resistance show that the non-
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`uniformity of heating is less than 4%. Since the heated
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`stainless steel sheet is Vertical, it is necessary to esti-
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`mate the effect of the buoyancy force. In a typical test
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`condition, Gr,_/Rc,2_ = 7.8 x 10*‘, where the Grashof
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`number. Gr1_ =g[}(T_,~T,,)L"/v3, and the Reynolds
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`number, Re,_ = UOL/v. ln above estimate, the charac-
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`teristic length L is the sheet width, the typical tem-
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`perature difference T, —~ T, is 40°C, thejet exit velocity
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`(/2, is l4 m s’ ', and other parameters have the standard
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`values for the quiescent air. Obviously, since Gr,_.«"
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`Ref << l, the buoyancy effect is small and can be neg-
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`lected [I4].
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`The temperaturesensitive fluorescent paint tech-
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`nique was used to measure surface temperature 72.
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`Fluorescence is a photoluminescencc process whereby
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`the molecules ofa fluorophore substance absorb light
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`of a particular wavelength and emit radiation of a
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`longer wavelength by losing their excitation energy.
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`The fluorescence intensity can be affected by so-called
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`thermal quenching and consequently depends on tem-
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`perature. Hence,
`temperature can be measured by
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`detecting the fluorescence intensity 1(T). The prin-
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`ciples of the fluorescent paint technique are discussed
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`in detail by Liu et a1. [lS—l7].
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`Page 2 of 12
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`Excited circular impinging jet
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`3697
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`In this study, a fluorescent paint, europium thenoyl-
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`trifluoroacetonate (EUTTA) in a polymer solution
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`(dope for painting model airplane) was used. For the
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`EuTTA-dope paint, the calibration relation between
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`and
`relative
`fluorescent
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`temperature
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`I(T)/I(T,) was experimentally determined, where the
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`reference temperature T, equals the ambient
`tem-
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`perature (22°C). A fourth-order polynomial fit of cali-
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`bration data is given by
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`I(T)/I(T.) = am
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`where
`a2 =
`a. = —0.0303419,
`a0 = 1.8723459,
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`—8.657407 X10“.
`a3 = 2.308471 x 10” and a4 =
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`—- 1.40501 x 10”. The EuTTA-dope paint (about 10
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`pm thick) was coated on the 0.05 mm thick white
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`Mylar film attached on the backside (relative to the
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`impingement side) of the stainless steel sheet. The
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`illumination source for exciting the fluorophore mol-
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`ecules was provided by an ultraviolet lamp. The flu-
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`orescence intensity image was taken by a CCD video
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`camera and recorded by a VCR. Then,
`the image
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`was digitized by a frame grabber with 512 x 512 pixel
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`spatial resolution and was converted into the surface
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`temperature map using the calibration relation. Once
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`T. is known, the local heat transfer coeflicient h can
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`be calculated from the definition /1: Q,/(T,-Tm).
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`The accuracy of the fluorescent paint technique has
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`been estimated by Liu et al. [18]. Error in temperature
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`measurement using the EuTTA-dope paint is i 08°C.
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`The low value of T,— T,0 is about 10°C. The uncer-
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`tainty of Q, is about i4'Vo. Hence, according to the
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`root—sum-square method,
`the uncertainty in cal-
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`culating h is about i9%.
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`The flush-mount hot-film sensor (TSI 1237) was
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`adapted for measurement of the surface heat transfer
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`fluctuation. The sensor is mounted on a movable plas-
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`tic target plate that is traversed relative to the nozzle in
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`the transverse direction. From the thermal equilibrium
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`relation of the hot—film element connected with a con-
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`stant temperature anemometer, the convective heat
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`transfer rate Q from the hot-film can be expressed as
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`Q = C(E‘—E§). where E is the output voltage of the
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`anemometer, E0 is the voltage when Q = 0 and C is a
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`constant. In shear flow, the convective heat transfer
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`rate Q from the film is proportional to the cubic root
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`of the wall shearing stress [19, 20]. Hence, measure-
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`ments of Q also reveal the local properties of flow
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`near the surface. For small heat transfer fluctuations,
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`Q’ z ZCEE’, where Q’
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`(r.m.s.) fluctuation of the convective heat transfer rate
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`and E’ is the r.m.s. fluctuation of the voltage.
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`FLOW CHARACTERISTICS
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`Free jet
`Velocity measurements for a free jet were carried
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`out using a single hot-wire probe in order to provide
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`information about the free jet itself. The centerline
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`velocity decreases slightly with the streamwise dis-
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`tance x and the potential core remains when x/D < 4.
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`The centerline turbulence intensity is about 0.4% at
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`the exit and reaches a maximum level of 9.5% at
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`x/D = 5.5. The boundary layer at the nozzle lip is
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`laminar. The normalized velocity u/Un at the nozzle
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`at
`lip measured
`different Reynolds
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`(Rep = 7170, 9700 and 12 300) has a near-Blasius pro-
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`file when a nondimensional coordinate y./60 is used,
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`where y, is the normal distance from the inner surface
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`of the nozzle, U0 is the exit velocity and 90 is the
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`initial momentum thickness. At Rel) = 7170,9700 and
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`12 300, the values of 80 are 0.172, 0.161 and 0.137 mm,
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`respectively. Since 00/D << 1, the boundary layer at the
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`nozzle lip is nearly two-dimensional.
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`The development of the shear layer downstream of
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`the nozzle edge is initially dominated by the Kelvin-
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`Helmholtz instability mechanism. Since 90 << D. the
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`initial shear layer of a circular jet can be approximated
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`as being a two-dimensional mixing layer. Hence. if the
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`disturbances are small, classical hydrodynamic stab-
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`ility theory can describe satisfactorily the initial evol-
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`ution of the instability wave in the mixing layer [21].
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`The instability waves grow exponentially with down-
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`stream distance and an important stability charac-
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`teristic is
`the spatial amplification rate —oc, =
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`d[ln(u’/U[,)]/dx, where a,- is the imaginary part of the
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`complex wave number, x is the streamwise coordinate
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`and u’ is the streamwise perturbation velocity. The
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`spatial amplification rate is a function of
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`frequency. By introducing a weak perturbation, ~oz,~
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`was determined experimentally within the linear
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`unstable region (x/D = 0.25-0.63) at Ren = 12300.
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`As shown in Fig. 2(a), the dimensionless amplification
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`growth rate —o:,B depends on the nondimensional
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`excitation frequency f,0/U0, where f, is the excitation
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`frequency and the local momentum thickness 0 is
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`0.165 mm. The experimental data are in agreement
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`with a theoretical calculation by Monkewitz and
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`Huerre [22] for the Blasius mixing layer. The measured
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`natural frequency fl, of the unexcited jet is 1400 Hz
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`(f;,6/U0 = 0.016 or f;,D/U0 = 1.23) at ReD = 12 300.
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`which coincides with the theoretical value of the most
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`amplified wave. As the shear layer develops and 6
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`grows, the properties of the jet should be scaled by
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`the length scale D. Over a range of x/D = 0.5-3.8, the
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`dimensionless natural frequency fi,D/U0 of the unex-
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`cited jet decreases from 1.23 near the exit to 0.61
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`at x/D = 2.5, as shown in Fig. 2(b). The stepwise
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`evolution of the vortex passage frequency is similar to
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`Kibens’ results [23] for an excited jet. Although the
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`‘jet column mode’ in the test is twice the value of
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`fl)/U0 = 0.3 reported by Crow and Champagne [24],
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`it is close tofD/ U0 = 0.5 given by Browand and Laufer
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`[25]. In fact, the ‘jet column mode’ measured in vari-
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`ous experiments appears to vary widely from 0.25 to
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`0.85 [26].
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`Impinging jet
`In contrast with the free jet in which 00 and D are
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`the two characteristic length scales, the impinging jet
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`Page 3 of 12
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`0.16
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`T. LIU and J. P. SULLIVAN
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`3.0
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`—— theoretical growth rate
`(Mmkewitz & Hume 1982)
`present measurement
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`0
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`2.5
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`0.14
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`0.12
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`0.10
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`0.08
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`0.06
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`0.04
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`0.02
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`natural frequency
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`#6000514
`first vortex pairing
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`2
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`0.00
`0.00
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`0.01
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`0.02
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`0.03
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`0.04
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`0.05
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`fee/U0
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`H/D
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`(8)
`(a) initial free jet shear layer spatial
`Fig. 2. Frequency characteristics of flow when Re” : 12300:
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`amplification ratc. (b) natural frequencies of free and impinging jets.
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`(D)
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`introduces an additional length scale: the no77le—to—
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`plate spacing H. At small H/D. the natural frequencies
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`of the impinging jet may dilfer from the free jet
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`because of the presence of the plate. The natural fre-
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`quency/,‘, ofthe unexeited impingingjet was detected
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`by a hot—film sensor flush-mounted on the target plate
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`at r/D = 0.7. In Fig. 2(b). the nondimensional natural
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`frequency fj,D/U‘,
`in the impinging jet is compared
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`with that in the free jet at Rel, : 12300. The natural
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`frequency of the impinging jet coincides with that of
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`the free jet when H/D > 1.2, and tends to increase
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`when H/D becomes smaller. When H/D = 0.8——l.2.
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`two peaks can be observed in the power spectrum of
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`the hot-film signal. Their frequencies are different until
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`two modes merge into the dominant mode of the free
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`jet at H/D : 1.2. The mechanisms generating the two
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`modes at small H/D are unclear.
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`The mean local streamwise velocity and r.m.s. flue-
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`tuating velocity in the wall-jet region were measured
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`at r/D = 0.79.
`l.l and 1.4 when H/D 2 l.l25 and
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`Rep = 12 300. The mean local streamwise velocity dis-
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`tributions along the normal direction to the wall indi-
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`cate that the wall—jet thickness is of the order of D/'4.
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`Here, D/4 is the wall—jet thickness at r/D = 0.5 for an
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`inviscid axisymmetric impinging jet. The maximum
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`local streamwise velocity llm, almost equals the jet
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`exit velocity U., in r/D = 0.79—l .1. This suggests that
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`the potential core persists in this region, although it is
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`defiected and spread along the radial direction by the
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`target plate. The potential core separates the outer
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`shear layer and the wall boundary layer, constituting
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`a ‘sandwich’ structure ofthree flow regimes. The outer
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`shear layer occupies most of the wall—jet. The outer
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`shear layer has an approximate hyperbolic tangent
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`profile u/um“ = 0.5[l + tanh(§)] at r./D = 0.79 and LI.
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`the normalized coordinate Q : 2(_1'.,. —_\')/6,.,.
`Here.
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`where y is the coordinate normal to the plate wall. yu ,—,
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`is the location at which u/u,m = 0.5. and 5,, = i4,,m."
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`(r‘ii,/r7_i')mM is the vorticity thickness. Thus, the outer
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`shear layer exhibits similar features to a two-dimen~
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`sional mixing layer [21, 26]. When r/D > 1.1, due to
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`viscous diffusion, the wall boundary layer merges with
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`the outer shear layer. Therefore. the L1 profile becomes
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`fully developed and the maximum of 14 decreases with
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`radial distance. The maximum values of the flue-
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`tuating velocity ii’/U‘, at r/D = 0.79, l.l and 1.4 are
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`0.14, 0.2 and 0.25, respectively.
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`UNEXCITED AND EXClTED JET IMPINGEMENT
`HEAT TRANSFER
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`ln the unexcited impingingjet. the stagnation—point
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`heat transfer Nun was measured as a characteristic
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`quantity for comparison with the well—known theor-
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`etical solution. When H/D g 2, the flow near the stag-
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`nation-point can be described by the laminar bound-
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`ary-layer solution. For a laminar stagnation-point
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`flow. the theoretical relation between Nu“ and R9,,
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`is Nui. = CPr”" (DB.,/b},)”Re,',‘2 [27]. where fl. =
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`(dU/dr),,(,._ Rep = UOD/v. U is the velocity of the
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`potential flow outside of the stagnation-point, U0 is
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`thejet exit velocity and D is the diameter ofthe nozzle.
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`The constant C is 0.763 for the axisymmetric flow.
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`Based on the potential flow analysis, Shadlesky [28]
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`suggested
`that
`the velocity gradient parameter
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`Dfi,/U” = 37r/16 for an axisymmetric jet. Hence.
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`Nuo/(Pr‘”Re1',‘2) = 0.585. Figure 3 shows the stag-
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`nation—point heat transfer as a function of H/D. The
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`experimental data are in good agreement with the
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`theoretical value when H/D < 2. As the shear layer
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`develops downstream, the potential core diminishes
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`and the heat transfer data deviate from the theoretical
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`value. The maximum stagnation-point heat transfer is
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`attained for H/D = 6-8.
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`Effects of monochromatic excitation on the surface
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`heat transfer are studied when the average initial exci-
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`Page 4 of 12
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`

`
`Excited circular impinging jet
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`3699
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`0
`0
`A
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`R9,, - 12271
`Ren - 14560
`Ran - 15100
`
`,aa§3
`
`33
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`6
`.31 f__
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`Nu,/(Pr°-‘ne,,"‘)
`
`theoretical value - 0.585
`
`4
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`6
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`8
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`10
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`12
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`HID
`Fig. 3. Stagnation-point heat transfer as a function of H/D.
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`tation level is fixed at u’/U0 = 0.1%. Figure 4 shows
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`the two-dimensional Nusselt number
`(Nu) dis-
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`tributions of the impinging jets for the cases of
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`1750 Hz and no excitation when
`f, = 950 Hz,
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`H/D = 1.125 and Rel) = 12 300. The two-dimensional
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`transfer distributions are obtained using the
`heat
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`temperature-sensitive fluorescent paint
`technique.
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`the two-dimensional heat
`transfer dis-
`Clearly.
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`tribution is sensitive to the excitation frequency. The
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`transverse heat transfer distributions in the excited
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`impinging jet are plotted in Fig. 5 against that in the
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`unexcited impinging jet at H/D : 1.125. At./Q = 1750
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`Hz,
`the local heat
`transfer in the wa11—jet region
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`(1 < r/D < 2)
`is considerably enhanced compared
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`with that in the unexcited impinging jet. In contrast,
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`at a lower excitation frequency f; = 950 Hz, the local
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`heat transfer is reduced in the wa1l—jet region. Near
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`the stagnation-point (-1 < r/D <1),
`the mono-
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`chromatic excitation does not significantly aflect the
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`time-averaged heat transfer.
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`In order to characterize the heat transfer enhance-
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`ment or reduction in a wide domain of the excitation
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`frequencies, a local enhancement factor 11
`is intro-
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`dl1C€d~
`*1 = Q(fé)/Q(fe= 0)—1~ Where QUE) and
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`Q(f; = 0) are the local transfer rates of the impinging
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`jet with the excitation and without the excitation,
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`respectively. The positive 7] indicates the local heat
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`7]
`enhancement
`and the negative
`transfer
`the
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`reduction. The magnitude of 11 represents the pro-
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`portion of the enhancement or reduction. Figure 6
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`shows the frequency-dependence of 97 obtained with
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`a flush-mount hot-film sensor at a particular radial
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`location r/D = 1.53, where the local heat transfer is
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`very sensitive to the excitation. Significant heat trans-
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`fer enhancement can be observed in a certain range
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`of frequencies when 0.875 S H/D S 2. The maximum
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`enhancement of the local heat transfer is about 10%.
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`When H/D < 0.625, no obvious heat
`transfer
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`enhancement is detected at any excitation frequency.
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`The frequency band in which the heat
`transfer
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`reduction is attained becomes narrow and eventually
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`diminishes as H/D increases. When H/D > 3, neither
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`enhancement nor reduction of the local heat transfer
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`is found. In Fig. 6, the natural frequency fl, of the
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`impinging jet is marked by an arrow. An important
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`observation is that the heat transfer enhancement may
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`occur when f, is close to 1,, and the heat transfer
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`reduction may happen when fc is close to _f,',/2. The
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`causes of the heat transfer enhancement and reduction
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`will be explored in the following sections.
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`RELATIONSHIP BETWEEN FLOW STRUCTURES
`
`Vortical structures and their effects on heat transfer
`In order to understand the relationship between the
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`flow structures and heat
`transfer,
`the smoke vis-
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`ualization was performed. The smoke from a cigarette
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`smoke generator was gently introduced through a 1
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`mm diameter TYGON tube into the flow at the nozzle
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`lip. A strobe light placed behind a glass target plate
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`was used to illuminate the flow structures through a
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`narrow slot. Four successive photos of Fig. 7 show
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`the stable pairing process of the ring vortices at
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`f; = 950 Hz when H/D = 1.125 and Rer, = 12300,
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`which corresponds to the case of the heat transfer
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`reduction. The shear layer starts to roll up to form the
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`discrete vortices before it impinges on the plate wall.
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`Then, the vortices move in the radial direction along
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`the wall. Because the excitation frequency fc is close
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`to the subharmonic of the natural frequency, two vor-
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`tices merge to form a bigger and stronger vortex at
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`r/D = 1.7. The coalescence of two vortices is similar
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`to that in the free jet, except that the trajectories of
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`the vortices are deflected by the plate. After the vortex
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`pairing, the resulting strong vortex in the outer shear
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`layer induces a counter-rotating secondary vortex
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`from the boundary layer at
`r/D = l.8—2.0. The
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`appearance of the secondary vortex can be identified
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`in photos 1 and 4 of Fig. 7. The secondary vortices
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`induced by the large-scale vortices
`in a round
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`impinging jet have been observed by Popiel and Trass
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`[10]. This phenomena is also referred to the vortex-
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`induced unsteady separation which is initiated by the
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`unsteady adverse pressure gradient produced by the
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`primary vortex [8]. The location of the vortex-induced
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`unsteady separation coincides with the valley of the
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`heat transfer distribution (r/D = 1.8—2.0) at _/"Q = 950
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`Hz in Fig. 5. This suggests that the vortex-induced
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`unsteady separation may induce the local heat transfer
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`reduction. A significant decrease in heat transfer rate
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`was also found by Rivir er al.
`[29]
`in a region of
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`turbulent separation induced by an adverse pressure
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`gradient on a Hat surface.
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`In contrast with the case of]; = 950 Hz, the 1750
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`Hz excitation produces ‘intermittent’ vortex pairing
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`rather than the stable vortex pairing, as shown in Fig.
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`8(a). The video tape indicates that the vortices jitter
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`in space during the intermittent vortex pairing
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`although thejittering cannot be seen in a single frame
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`of the photo in Fig. 8(a). In this case, the time trace
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`Page 5 of 12
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`

`
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`
`T. LIU and J. P. SULLIVAN
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`Fig. 4. Two-dimensional Nusselt number distributions of excited impinging jet when H/D = 1.125 and
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`Re” = 12300: (a)/'. — 950 Hz, (b)_/;. = 1750 Hz, (c) unexcited.
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`of the hot-film signal shows that the subharmonic
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`wave occurs intermittently. Also. the phase difference
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`between the excited fundamental and self-generated
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`subharmonic waves randomly drifts. Instead ofa well-
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`organized vortex,
`the intermittent vortex pairing
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`forms a chaotic ‘lump eddy‘ which contains a great
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`deal of small-scale random turbulence (the term ‘eddy‘
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`is used instead of ‘vortcx“ since the flow structure is
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`not well-organized). The vortical structures become
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`less organized after the intermittent vortex pairing. In
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`this case. the flow Visualization does not show obvious
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`vortex-induced separation. The location of the chaotic
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`Page 6 of 12
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`Unexcited
`
`———- f_ = 950 Hz
`...... .. f‘ = 1750 Hz
`
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`
`Excited circular impinging jet
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`)1
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`Fig. 5. Transverse Nusselt number distributions of excited
`
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`impinging jet when H/D = 1.125 and Rep = 12 300.
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`2
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`11
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`0.15
`0.10
`0.05
`0.00
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`T‘ 0.00
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`0.0 0.5
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`1.0
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`2.0 2.5 3.0
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`3.5
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`ip/U0
`Fig. 6. Heat transfer enhancement factor as a function of
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`excitation frequency at r/D = 1.53 when R2,) = 12 300.
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`‘lump eddy’ just corresponds to the second peak of the
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`heat transfer distribution (r/D = 1.5-1.8) at f, : 1750
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`Hz in Fig. 5. This suggests that an increase in the
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`random turbulence causes the heat transfer enhance-
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`ment. A similar observation has been reported by
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`Kataoka et al. [12]. They found that the turbulent,
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`less coherent structure can enhance the stagnation-
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`point heat transfer more eflectively than the non-
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`turbulent coherent structure with the periodic flue-
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`tuation. For
`the
`unexcited
`impinging jet
`at
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`no 0.,“
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`3
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`)
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`2.5
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`Fig. 7. Successive photos of stable vortex pairing in excited
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`impinging jet at f, = 950 Hz when H/D = 1.125 and
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`R2,, = 12 300.
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`H/ D = 1.125, the organized vortices are shown in Fig.
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`8(b). No vortex pairing is observed in this case.
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`It is desirable to discuss effects of the large-scale
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`organized vortices and small-scale random turbulence
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`transfer in the wall—jet region. The heat
`on heat
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`flux Q is expressed as a sum of
`three terms
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`Q = —kéf/6y+pcPv;T;+pcpv{c7TC, where the sub-
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`scripts c and ic represent the coherent component
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`induced by the organized vortices and incoherent
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`component caused by the small-scale random tur-
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`bulence, respectively. The first term in the right-hand
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`side is the mean heat flux, the second term represents
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`the coherent part of the turbulent heat flux, and the
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`third term denotes the incoherent part of the turbulent
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`heat flux. It should be emphasized that the first term
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`- k8 T"/6y is implicitly dependent on the coherent and
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`random fluctuating velocities, because these flue-
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`tuations modify the mean flow. For a hot wall, large-
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`Page 7 of 12
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`T, LIU and J. P. SULLIVAN
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`from separation. but also significantly increases the
`incoherent heat flux {)(‘pl.‘;cT,/C. Overall, the local heat
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`transfer is enhanced in this case.
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`Heat‘ transfer spectra
`The dynamic aspects of the impinging jet can be
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`further studied by examining spectra of the time-
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`dependent heat transfer fluctuation. The local heat
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`transfer fluctuation was measured by a flush—mount
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`hot-film sensor. The spectrum development of the
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`relative heat transfer fluctuation Q"/QI, at different
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`radial locations on the wall is shown in Fig. 9(a) for
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`the case of]; : 950 Hz and H10 2 L125 (heat trans-
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`fer reduction case). where Q‘, is the mean heat transfer
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`rate at the stagnation—point. For comparison. the cor-
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`responding heat
`transfer spectra of the unexcited
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`impinging jet are also plotted. In all spectra for the
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`excited impingingjet the excitation frequency]; com-
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`ponent is dominant. although the harmonics and weak
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`randomness are present. Since /Q. is close to the sub-
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`harmonic of the natural frequency, the excitation pro-
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`motes vortex pairing as indicated by the flow vis-
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`ualization. Compared with the unexcited case. the 950
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`Hz excitation considerably suppresses the broad spec-
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`tral components ofthe small-scale random turbulence
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`such that the well-defined characteristic frequencies f“
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`is still distinguishable at r/D : 1.85. This is consistent
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`with the flow visualization observation which indi-
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`cates the existence of the well—organized vortices at
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`r,'[) = 1.8 after stable pairing. Figure l0(a) shows the
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`spatial evolution of two dominant modes _f; and 2];
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`along the radial direction. The amplitudes of the 1;.
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`and 2]; modes grow exponentially at the beginning.
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`reach a maximum at r/D : l and then decay. The
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`fluctuation intensity that
`includes the con-
`total
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`tributions from all spectral components is also given
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`for comparison. The amplitude difference between the
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`total
`intensity and discrete modes represents the
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`amount of randomness. Figure l0(a) indicates that
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`the f_. mode is so dominant that the flow is highly
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`coherent for r,/D : 0.5-1.0. Only after r/D 2 1.5. do
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`the broad spectral components of the small-scale ran-
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`dom turbulence beeome evident. The heat transfer
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`reduction occurs after the dominant modes saturate.
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`Note that thef; spectral component has a local mini-
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`mum at r/D 2 1.75 where the greatest heat transfer
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`reduction is attained. From the flow visualization
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`photos in Fig. 7, it can be found that the location of
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`the amplitude minimum at r/‘D = 1.75 corresponds to
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`the separation point between the primary vortex and
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`secondary vortex. The
`secondary
`induced
`the
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`maximum of the]; spectral component at r/D = 2 is
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`caused by the generation ofthe secondary vortex. The
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`spectral analysis supports the observation that the
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`vortex-induced separation causes the local heat trans-
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`fer reduction.
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`transfer enhancement
`When /L. = 1750 Hz (heat
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`the subharmonic component fa"/2 is spon-
`case).
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`taneously generated and has a comparable amplitude
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`to the excited fundamental mode 1; Over a range of
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`0.5
`r/D
`2.5
`1.5
`Fig. 8. Vertical structures ofimpingingjet when H/D : 1.125
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`and Rep = 12300: (a)_fi : 1750 Hz. (b) unexcited.
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`scale