`
`Samsung Exhibit 1023
`Samsung Electronics Co., Ltd. v. Daniel L. Flamm
`
`
`
`
`
`
`
`
`
`
`
`
`
`T. LIU and .l. P. SULLIVAN
`
`
`
`
`
`
`
`NOMENCLATURE
`
`
`
`
`
`
`
`
`']
`
`
`
`
`specific heat [J kg’ ' K E]
`
`
`
`
`
`
`nonle diameter [m]
`
`
`
`output voltage of anemometer [Volt]
`
`
`
`
`E without flow [Volt]
`
`
`
`
`voltage fluctuation [Volt]
`
`
`natural frequency [Hz]
`
`
`
`excitation frequency [H7]
`
`
`
`local convective heat transfer
`
`
`
`coeflicient [W in’ 3 K "]
`
`
`
`
`
`
`nozzle-to-plate spacing [rn]
`
`
`fluorescence intensity [J 5
`
`
`
`thermal conductivity of air
`
`
`
`[W m ' K ']
`
`
`
`Nusselt number, /1D/k
`
`
`stagnation-point Nusselt number
`
`
`
`Prandtl number, pcpv,/k
`
`
`local convective heat transfer rate
`
`
`
`
`[W m’ 3]
`
`
`convective heat transfer rate at
`
`
`
`
`stagnation—point [W m 3]
`
`
`
`heat flux from heated steel sheet
`
`
`
`
`
`surface [W m ' 3]
`
`
`
`
`local convective heat transter
`
`
`
`fluctuation [W 111*]
`
`
`
`radial coordinate [in]
`
`
`
`
`
`
`
`correlation coefficient,
`
`
`Q'(I+I. 0)u’(I-.1‘)/(Q'H’)
`Reynolds number, U.,D/v
`
`
`temperature [°C]
`
`
`reference temperature ["C]
`
`
`
`temperature of heated steel sheet
`
`
`
`
`surface [“C]
`
`
`ambient temperature [ C]
`
`
`
`
`temperature fluctuatio11[ C]
`
`
`
`jet exit velocity [m s"]
`
`
`
`
`
`
`']
`streamwise velocity [in s
`
`
`
`
`
`streamwise fluctuating velocity [m s
`
`
`
`
`fluctuating velocity normal to wall
`
`
`
`
`
`lm 8”]
`
`
`streamwise cordinate in free jet [in]
`
`
`
`
`
`coordinate normal to wall [in].
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Greek symbols
`
`
`-1,
`spatial amplification rate [in ']
`
`
`
`
`
`
`factor of heat transfer enhancement.
`:1
`
`
`
`
`
`Qt./L)/QU; = 0)—l
`kinematic viscosity [m3 s’ 1]
`
`
`
`momentum thickness [In]
`
`
`
`initial momentum thickness [In]
`
`
`
`density of air [kg m"‘].
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`7]
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`heated steel sheet
`
`1 aifflgw
`
`painted side
`
`CCD Camera
`
`
`
`
`
`
`
`
`
`Fig.
`
`
`
`(b)
`
`1 Experimental set-up: (a) jet facility,
`
`
`
`
`
`system,
`
`
`(13) coordinate
`
`
`
`
`
`
`maximum deformation of the sheet due to low speed
`
`
`
`
`
`
`
`
`
`jet impingement is less than 0.1 mm. Note that the jet
`
`
`
`
`
`
`
`
`
`
`
`impingement cooling could cause spatial variation of
`
`
`
`
`
`
`
`the sheet resistivity and consequently lead to non—
`
`
`
`
`
`
`
`
`uniform heating. The measurements of the spatial
`
`
`
`
`
`
`
`variations of the sheet resistance show that the non-
`
`
`
`
`
`
`
`
`
`uniformity of heating is less than 4%. Since the heated
`
`
`
`
`
`
`
`
`
`
`stainless steel sheet is Vertical, it is necessary to esti-
`
`
`
`
`
`
`
`
`
`
`mate the effect of the buoyancy force. In a typical test
`
`
`
`
`
`
`
`
`
`
`
`condition, Gr,_/Rc,2_ = 7.8 x 10*‘, where the Grashof
`
`
`
`
`
`
`
`
`
`number. Gr1_ =g[}(T_,~T,,)L"/v3, and the Reynolds
`
`
`
`
`number, Re,_ = UOL/v. ln above estimate, the charac-
`
`
`
`
`
`
`teristic length L is the sheet width, the typical tem-
`
`
`
`
`
`
`
`
`
`
`perature difference T, —~ T, is 40°C, thejet exit velocity
`
`
`
`
`
`
`
`
`
`
`(/2, is l4 m s’ ', and other parameters have the standard
`
`
`
`
`
`
`
`
`
`
`
`values for the quiescent air. Obviously, since Gr,_.«"
`
`
`
`
`
`
`
`
`Ref << l, the buoyancy effect is small and can be neg-
`
`
`
`
`
`
`
`
`
`
`lected [I4].
`
`
`The temperaturesensitive fluorescent paint tech-
`
`
`
`
`nique was used to measure surface temperature 72.
`
`
`
`
`
`
`
`Fluorescence is a photoluminescencc process whereby
`
`
`
`
`the molecules ofa fluorophore substance absorb light
`
`
`
`
`
`
`of a particular wavelength and emit radiation of a
`
`
`
`
`
`
`
`
`longer wavelength by losing their excitation energy.
`
`
`
`
`
`
`The fluorescence intensity can be affected by so-called
`
`
`
`
`
`
`
`thermal quenching and consequently depends on tem-
`
`
`
`
`
`
`perature. Hence,
`temperature can be measured by
`
`
`
`
`
`
`detecting the fluorescence intensity 1(T). The prin-
`
`
`
`
`
`ciples of the fluorescent paint technique are discussed
`
`
`
`
`
`
`
`in detail by Liu et a1. [lS—l7].
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 2 of 12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Excited circular impinging jet
`
`
`
`
`
`
`3697
`
`
`
`In this study, a fluorescent paint, europium thenoyl-
`
`
`
`
`
`
`trifluoroacetonate (EUTTA) in a polymer solution
`
`
`
`
`
`(dope for painting model airplane) was used. For the
`
`
`
`
`
`
`
`
`EuTTA-dope paint, the calibration relation between
`
`
`
`
`
`and
`relative
`fluorescent
`intensity
`temperature
`
`
`
`
`I(T)/I(T,) was experimentally determined, where the
`
`
`
`
`reference temperature T, equals the ambient
`tem-
`
`
`
`
`
`
`perature (22°C). A fourth-order polynomial fit of cali-
`
`
`
`
`
`
`
`bration data is given by
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`I(T)/I(T.) = am
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`where
`a2 =
`a. = —0.0303419,
`a0 = 1.8723459,
`
`
`
`
`
`
`
`
`
`—8.657407 X10“.
`a3 = 2.308471 x 10” and a4 =
`
`
`
`
`
`
`
`
`
`
`
`—- 1.40501 x 10”. The EuTTA-dope paint (about 10
`
`
`
`
`
`
`
`
`pm thick) was coated on the 0.05 mm thick white
`
`
`
`
`
`
`
`
`
`Mylar film attached on the backside (relative to the
`
`
`
`
`
`
`
`
`impingement side) of the stainless steel sheet. The
`
`
`
`
`
`
`
`illumination source for exciting the fluorophore mol-
`
`
`
`
`
`
`ecules was provided by an ultraviolet lamp. The flu-
`
`
`
`
`
`
`
`
`orescence intensity image was taken by a CCD video
`
`
`
`
`
`
`
`camera and recorded by a VCR. Then,
`the image
`
`
`
`
`
`
`
`
`was digitized by a frame grabber with 512 x 512 pixel
`
`
`
`
`
`
`
`
`
`spatial resolution and was converted into the surface
`
`
`
`
`
`
`
`temperature map using the calibration relation. Once
`
`
`
`
`
`
`T. is known, the local heat transfer coeflicient h can
`
`
`
`
`
`
`
`
`be calculated from the definition /1: Q,/(T,-Tm).
`
`
`
`
`
`
`
`The accuracy of the fluorescent paint technique has
`
`
`
`
`
`
`
`
`been estimated by Liu et al. [18]. Error in temperature
`
`
`
`
`
`
`
`
`measurement using the EuTTA-dope paint is i 08°C.
`
`
`
`
`
`
`
`
`The low value of T,— T,0 is about 10°C. The uncer-
`
`
`
`
`
`
`
`
`
`
`tainty of Q, is about i4'Vo. Hence, according to the
`
`
`
`
`
`
`
`
`
`
`
`root—sum-square method,
`the uncertainty in cal-
`
`
`
`
`
`
`culating h is about i9%.
`
`
`
`
`The flush-mount hot-film sensor (TSI 1237) was
`
`
`
`
`
`
`
`adapted for measurement of the surface heat transfer
`
`
`
`
`
`
`
`
`fluctuation. The sensor is mounted on a movable plas-
`
`
`
`
`
`
`
`
`tic target plate that is traversed relative to the nozzle in
`
`
`
`
`
`
`
`
`
`
`
`the transverse direction. From the thermal equilibrium
`
`
`
`
`
`
`
`relation of the hot—film element connected with a con-
`
`
`
`
`
`
`
`
`stant temperature anemometer, the convective heat
`
`
`
`
`
`
`transfer rate Q from the hot-film can be expressed as
`
`
`
`
`
`
`
`
`
`
`Q = C(E‘—E§). where E is the output voltage of the
`
`
`
`
`
`
`
`
`
`
`
`
`
`anemometer, E0 is the voltage when Q = 0 and C is a
`
`
`
`
`
`
`
`
`
`
`
`
`constant. In shear flow, the convective heat transfer
`
`
`
`
`
`
`
`
`rate Q from the film is proportional to the cubic root
`
`
`
`
`
`
`
`
`
`
`
`of the wall shearing stress [19, 20]. Hence, measure-
`
`
`
`
`
`
`
`
`
`ments of Q also reveal the local properties of flow
`
`
`
`
`
`
`
`
`
`
`near the surface. For small heat transfer fluctuations,
`
`
`
`
`
`
`
`
`Q’ z ZCEE’, where Q’
`is
`the root-mean-square
`
`
`
`
`
`(r.m.s.) fluctuation of the convective heat transfer rate
`
`
`
`
`
`
`
`
`and E’ is the r.m.s. fluctuation of the voltage.
`
`
`
`
`
`
`
`
`
`
`FLOW CHARACTERISTICS
`
`Free jet
`Velocity measurements for a free jet were carried
`
`
`
`
`
`
`
`out using a single hot-wire probe in order to provide
`
`
`
`
`
`
`
`
`information about the free jet itself. The centerline
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`velocity decreases slightly with the streamwise dis-
`
`
`
`
`
`
`tance x and the potential core remains when x/D < 4.
`
`
`
`
`
`
`
`The centerline turbulence intensity is about 0.4% at
`
`
`
`
`
`
`
`the exit and reaches a maximum level of 9.5% at
`
`
`
`
`
`
`
`
`
`x/D = 5.5. The boundary layer at the nozzle lip is
`
`
`
`
`
`
`
`
`
`laminar. The normalized velocity u/Un at the nozzle
`
`
`
`
`
`
`at
`lip measured
`different Reynolds
`numbers
`
`
`
`
`
`(Rep = 7170, 9700 and 12 300) has a near-Blasius pro-
`
`
`
`
`
`
`
`
`file when a nondimensional coordinate y./60 is used,
`
`
`
`
`
`
`where y, is the normal distance from the inner surface
`
`
`
`
`
`
`
`
`
`of the nozzle, U0 is the exit velocity and 90 is the
`
`
`
`
`
`
`
`
`
`
`
`initial momentum thickness. At Rel) = 7170,9700 and
`
`
`
`
`
`
`
`12 300, the values of 80 are 0.172, 0.161 and 0.137 mm,
`
`
`
`
`
`
`
`
`
`
`
`respectively. Since 00/D << 1, the boundary layer at the
`
`
`
`
`
`
`
`
`nozzle lip is nearly two-dimensional.
`
`
`
`
`
`The development of the shear layer downstream of
`
`
`
`
`
`
`
`
`the nozzle edge is initially dominated by the Kelvin-
`
`
`
`
`
`
`
`
`
`Helmholtz instability mechanism. Since 90 << D. the
`
`
`
`
`
`
`
`
`initial shear layer of a circular jet can be approximated
`
`
`
`
`
`
`
`
`
`as being a two-dimensional mixing layer. Hence. if the
`
`
`
`
`
`
`
`
`disturbances are small, classical hydrodynamic stab-
`
`
`
`
`
`
`ility theory can describe satisfactorily the initial evol-
`
`
`
`
`
`
`
`
`ution of the instability wave in the mixing layer [21].
`
`
`
`
`
`
`
`
`
`
`The instability waves grow exponentially with down-
`
`
`
`
`
`
`
`stream distance and an important stability charac-
`
`
`
`
`
`
`
`teristic is
`the spatial amplification rate —oc, =
`
`
`
`
`
`
`
`
`d[ln(u’/U[,)]/dx, where a,- is the imaginary part of the
`
`
`
`
`
`
`
`
`complex wave number, x is the streamwise coordinate
`
`
`
`
`
`
`
`and u’ is the streamwise perturbation velocity. The
`
`
`
`
`
`
`
`
`spatial amplification rate is a function of
`the
`
`
`
`
`
`
`
`
`frequency. By introducing a weak perturbation, ~oz,~
`
`
`
`
`
`
`was determined experimentally within the linear
`
`
`
`
`
`
`unstable region (x/D = 0.25-0.63) at Ren = 12300.
`
`
`
`
`
`
`As shown in Fig. 2(a), the dimensionless amplification
`
`
`
`
`
`
`
`
`growth rate —o:,B depends on the nondimensional
`
`
`
`
`
`
`excitation frequency f,0/U0, where f, is the excitation
`
`
`
`
`
`
`
`
`frequency and the local momentum thickness 0 is
`
`
`
`
`
`
`
`
`0.165 mm. The experimental data are in agreement
`
`
`
`
`
`
`
`
`with a theoretical calculation by Monkewitz and
`
`
`
`
`
`
`
`Huerre [22] for the Blasius mixing layer. The measured
`
`
`
`
`
`
`
`
`
`natural frequency fl, of the unexcited jet is 1400 Hz
`
`
`
`
`
`
`
`
`
`
`(f;,6/U0 = 0.016 or f;,D/U0 = 1.23) at ReD = 12 300.
`
`
`
`
`
`
`
`which coincides with the theoretical value of the most
`
`
`
`
`
`
`
`
`
`amplified wave. As the shear layer develops and 6
`
`
`
`
`
`
`
`
`
`grows, the properties of the jet should be scaled by
`
`
`
`
`
`
`
`
`
`
`the length scale D. Over a range of x/D = 0.5-3.8, the
`
`
`
`
`
`
`
`
`
`dimensionless natural frequency fi,D/U0 of the unex-
`
`
`
`
`
`cited jet decreases from 1.23 near the exit to 0.61
`
`
`
`
`
`
`
`
`
`
`at x/D = 2.5, as shown in Fig. 2(b). The stepwise
`
`
`
`
`
`
`
`
`
`
`evolution of the vortex passage frequency is similar to
`
`
`
`
`
`
`
`
`
`Kibens’ results [23] for an excited jet. Although the
`
`
`
`
`
`
`
`
`
`‘jet column mode’ in the test is twice the value of
`
`
`
`
`
`
`
`
`
`
`
`fl)/U0 = 0.3 reported by Crow and Champagne [24],
`
`
`
`
`
`
`
`
`it is close tofD/ U0 = 0.5 given by Browand and Laufer
`
`
`
`
`
`
`
`
`
`
`[25]. In fact, the ‘jet column mode’ measured in vari-
`
`
`
`
`
`
`
`
`
`
`ous experiments appears to vary widely from 0.25 to
`
`
`
`
`
`
`
`
`
`0.85 [26].
`
`
`Impinging jet
`In contrast with the free jet in which 00 and D are
`
`
`
`
`
`
`
`
`
`
`
`
`the two characteristic length scales, the impinging jet
`
`
`
`
`
`
`
`
`
`Page 3 of 12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`0.16
`
`T. LIU and J. P. SULLIVAN
`
`
`
`
`
`
`
`
`3.0
`
`—— theoretical growth rate
`(Mmkewitz & Hume 1982)
`present measurement
`
`0
`
`2.5
`
`
`
`0.14
`
`0.12
`
`0.10
`
`0.08
`
`0.06
`
`0.04
`
`0.02
`
`natural frequency
`
`
`
`#6000514
`first vortex pairing
`
`
`2
`
`0.00
`0.00
`
`0.01
`
`0.02
`
`0.03
`
`0.04
`
`0.05
`
`
`
`fee/U0
`
`H/D
`
`(8)
`(a) initial free jet shear layer spatial
`Fig. 2. Frequency characteristics of flow when Re” : 12300:
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`amplification ratc. (b) natural frequencies of free and impinging jets.
`
`
`
`
`
`
`
`
`
`
`
`
`(D)
`
`
`
`introduces an additional length scale: the no77le—to—
`
`
`
`
`
`
`
`plate spacing H. At small H/D. the natural frequencies
`
`
`
`
`
`
`
`
`of the impinging jet may dilfer from the free jet
`
`
`
`
`
`
`
`
`
`
`because of the presence of the plate. The natural fre-
`
`
`
`
`
`
`
`
`
`
`quency/,‘, ofthe unexeited impingingjet was detected
`
`
`
`
`
`
`
`
`by a hot—film sensor flush-mounted on the target plate
`
`
`
`
`
`
`
`
`
`at r/D = 0.7. In Fig. 2(b). the nondimensional natural
`
`
`
`
`
`
`
`
`
`frequency fj,D/U‘,
`in the impinging jet is compared
`
`
`
`
`
`
`
`with that in the free jet at Rel, : 12300. The natural
`
`
`
`
`
`
`
`
`
`
`
`
`frequency of the impinging jet coincides with that of
`
`
`
`
`
`
`
`
`
`the free jet when H/D > 1.2, and tends to increase
`
`
`
`
`
`
`
`
`
`
`when H/D becomes smaller. When H/D = 0.8——l.2.
`
`
`
`
`
`
`
`two peaks can be observed in the power spectrum of
`
`
`
`
`
`
`
`
`
`
`the hot-film signal. Their frequencies are different until
`
`
`
`
`
`
`
`
`two modes merge into the dominant mode of the free
`
`
`
`
`
`
`
`
`
`
`jet at H/D : 1.2. The mechanisms generating the two
`
`
`
`
`
`
`
`
`
`modes at small H/D are unclear.
`
`
`
`
`
`The mean local streamwise velocity and r.m.s. flue-
`
`
`
`
`
`
`
`
`tuating velocity in the wall-jet region were measured
`
`
`
`
`
`
`
`
`at r/D = 0.79.
`l.l and 1.4 when H/D 2 l.l25 and
`
`
`
`
`
`
`
`
`
`
`Rep = 12 300. The mean local streamwise velocity dis-
`
`
`
`
`
`
`
`
`
`tributions along the normal direction to the wall indi-
`
`
`
`
`
`
`
`
`
`cate that the wall—jet thickness is of the order of D/'4.
`
`
`
`
`
`
`
`
`
`
`Here, D/4 is the wall—jet thickness at r/D = 0.5 for an
`
`
`
`
`
`
`
`
`
`
`inviscid axisymmetric impinging jet. The maximum
`
`
`
`
`
`
`local streamwise velocity llm, almost equals the jet
`
`
`
`
`
`
`
`
`
`exit velocity U., in r/D = 0.79—l .1. This suggests that
`
`
`
`
`
`
`
`
`
`the potential core persists in this region, although it is
`
`
`
`
`
`
`
`
`
`
`defiected and spread along the radial direction by the
`
`
`
`
`
`
`
`
`
`target plate. The potential core separates the outer
`
`
`
`
`
`
`
`
`shear layer and the wall boundary layer, constituting
`
`
`
`
`
`
`
`
`a ‘sandwich’ structure ofthree flow regimes. The outer
`
`
`
`
`
`
`
`
`
`shear layer occupies most of the wall—jet. The outer
`
`
`
`
`
`
`
`
`
`shear layer has an approximate hyperbolic tangent
`
`
`
`
`
`
`
`profile u/um“ = 0.5[l + tanh(§)] at r./D = 0.79 and LI.
`
`
`
`
`
`
`
`
`
`
`the normalized coordinate Q : 2(_1'.,. —_\')/6,.,.
`Here.
`
`
`
`
`
`
`
`
`where y is the coordinate normal to the plate wall. yu ,—,
`
`
`
`
`
`
`
`
`
`
`
`is the location at which u/u,m = 0.5. and 5,, = i4,,m."
`
`
`
`
`
`
`
`
`
`
`
`(r‘ii,/r7_i')mM is the vorticity thickness. Thus, the outer
`
`
`
`
`
`
`
`
`
`shear layer exhibits similar features to a two-dimen~
`
`
`
`
`
`
`
`
`sional mixing layer [21, 26]. When r/D > 1.1, due to
`
`
`
`
`
`
`
`
`
`
`viscous diffusion, the wall boundary layer merges with
`
`
`
`
`
`
`
`
`the outer shear layer. Therefore. the L1 profile becomes
`
`
`
`
`
`
`
`
`
`fully developed and the maximum of 14 decreases with
`
`
`
`
`
`
`
`
`
`radial distance. The maximum values of the flue-
`
`
`
`
`
`
`
`
`tuating velocity ii’/U‘, at r/D = 0.79, l.l and 1.4 are
`
`
`
`
`
`
`
`
`
`0.14, 0.2 and 0.25, respectively.
`
`
`
`
`
`
`UNEXCITED AND EXClTED JET IMPINGEMENT
`HEAT TRANSFER
`
`
`
`ln the unexcited impingingjet. the stagnation—point
`
`
`
`
`
`
`heat transfer Nun was measured as a characteristic
`
`
`
`
`
`
`
`quantity for comparison with the well—known theor-
`
`
`
`
`
`
`
`etical solution. When H/D g 2, the flow near the stag-
`
`
`
`
`
`
`
`
`
`
`nation-point can be described by the laminar bound-
`
`
`
`
`
`
`
`
`ary-layer solution. For a laminar stagnation-point
`
`
`
`
`
`
`flow. the theoretical relation between Nu“ and R9,,
`
`
`
`
`
`
`is Nui. = CPr”" (DB.,/b},)”Re,',‘2 [27]. where fl. =
`
`
`
`
`
`(dU/dr),,(,._ Rep = UOD/v. U is the velocity of the
`
`
`
`
`
`potential flow outside of the stagnation-point, U0 is
`
`
`
`
`
`
`
`
`thejet exit velocity and D is the diameter ofthe nozzle.
`
`
`
`
`
`
`
`
`
`
`
`
`The constant C is 0.763 for the axisymmetric flow.
`
`
`
`
`
`
`
`
`
`Based on the potential flow analysis, Shadlesky [28]
`
`
`
`
`
`
`
`
`suggested
`that
`the velocity gradient parameter
`
`
`
`
`
`
`Dfi,/U” = 37r/16 for an axisymmetric jet. Hence.
`
`
`
`
`
`
`Nuo/(Pr‘”Re1',‘2) = 0.585. Figure 3 shows the stag-
`
`
`
`
`
`
`
`nation—point heat transfer as a function of H/D. The
`
`
`
`
`
`
`
`
`experimental data are in good agreement with the
`
`
`
`
`
`
`
`
`theoretical value when H/D < 2. As the shear layer
`
`
`
`
`
`
`
`
`
`develops downstream, the potential core diminishes
`
`
`
`
`
`
`and the heat transfer data deviate from the theoretical
`
`
`
`
`
`
`
`
`
`value. The maximum stagnation-point heat transfer is
`
`
`
`
`
`
`
`attained for H/D = 6-8.
`
`
`Effects of monochromatic excitation on the surface
`
`
`
`
`
`
`
`heat transfer are studied when the average initial exci-
`
`
`
`
`
`
`
`
`
`
`Page 4 of 12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Excited circular impinging jet
`
`
`
`
`
`
`3699
`
`
`
`0
`0
`A
`
`R9,, - 12271
`Ren - 14560
`Ran - 15100
`
`,aa§3
`
`33
`
`6
`.31 f__
`
`
`
`Nu,/(Pr°-‘ne,,"‘)
`
`theoretical value - 0.585
`
`4
`
`6
`
`8
`
`10
`
`12
`
`HID
`Fig. 3. Stagnation-point heat transfer as a function of H/D.
`
`
`
`
`
`
`
`
`
`tation level is fixed at u’/U0 = 0.1%. Figure 4 shows
`
`
`
`
`
`
`
`
`
`
`the two-dimensional Nusselt number
`(Nu) dis-
`
`
`
`
`
`tributions of the impinging jets for the cases of
`
`
`
`
`
`
`
`
`
`1750 Hz and no excitation when
`f, = 950 Hz,
`
`
`
`
`
`
`
`
`H/D = 1.125 and Rel) = 12 300. The two-dimensional
`
`
`
`
`
`
`
`
`transfer distributions are obtained using the
`heat
`
`
`
`
`
`
`
`temperature-sensitive fluorescent paint
`technique.
`
`
`
`
`the two-dimensional heat
`transfer dis-
`Clearly.
`
`
`
`
`
`
`tribution is sensitive to the excitation frequency. The
`
`
`
`
`
`
`
`
`transverse heat transfer distributions in the excited
`
`
`
`
`
`
`
`impinging jet are plotted in Fig. 5 against that in the
`
`
`
`
`
`
`
`
`
`
`
`unexcited impinging jet at H/D : 1.125. At./Q = 1750
`
`
`
`
`
`
`
`
`
`Hz,
`the local heat
`transfer in the wa11—jet region
`
`
`
`
`
`
`
`
`
`(1 < r/D < 2)
`is considerably enhanced compared
`
`
`
`
`
`
`
`
`with that in the unexcited impinging jet. In contrast,
`
`
`
`
`
`
`
`
`
`at a lower excitation frequency f; = 950 Hz, the local
`
`
`
`
`
`
`
`
`
`
`heat transfer is reduced in the wa1l—jet region. Near
`
`
`
`
`
`
`
`
`
`the stagnation-point (-1 < r/D <1),
`the mono-
`
`
`
`
`
`
`
`
`chromatic excitation does not significantly aflect the
`
`
`
`
`
`
`
`time-averaged heat transfer.
`
`
`
`In order to characterize the heat transfer enhance-
`
`
`
`
`
`
`
`
`ment or reduction in a wide domain of the excitation
`
`
`
`
`
`
`
`
`
`frequencies, a local enhancement factor 11
`is intro-
`
`
`
`
`
`
`
`
`dl1C€d~
`*1 = Q(fé)/Q(fe= 0)—1~ Where QUE) and
`
`
`
`
`
`
`
`
`Q(f; = 0) are the local transfer rates of the impinging
`
`
`
`
`
`
`
`
`
`
`
`jet with the excitation and without the excitation,
`
`
`
`
`
`
`
`
`respectively. The positive 7] indicates the local heat
`
`
`
`
`
`
`
`
`7]
`enhancement
`and the negative
`transfer
`the
`
`
`
`
`
`
`
`reduction. The magnitude of 11 represents the pro-
`
`
`
`
`
`
`
`
`portion of the enhancement or reduction. Figure 6
`
`
`
`
`
`
`
`
`shows the frequency-dependence of 97 obtained with
`
`
`
`
`
`
`a flush-mount hot-film sensor at a particular radial
`
`
`
`
`
`
`
`
`location r/D = 1.53, where the local heat transfer is
`
`
`
`
`
`
`
`
`very sensitive to the excitation. Significant heat trans-
`
`
`
`
`
`
`
`
`fer enhancement can be observed in a certain range
`
`
`
`
`
`
`
`
`
`of frequencies when 0.875 S H/D S 2. The maximum
`
`
`
`
`
`
`
`
`
`enhancement of the local heat transfer is about 10%.
`
`
`
`
`
`
`
`
`
`When H/D < 0.625, no obvious heat
`transfer
`
`
`
`
`
`enhancement is detected at any excitation frequency.
`
`
`
`
`
`
`
`The frequency band in which the heat
`transfer
`
`
`
`
`
`
`
`
`
`reduction is attained becomes narrow and eventually
`
`
`
`
`
`
`diminishes as H/D increases. When H/D > 3, neither
`
`
`
`
`
`
`enhancement nor reduction of the local heat transfer
`
`
`
`
`
`
`
`is found. In Fig. 6, the natural frequency fl, of the
`
`
`
`
`
`
`
`
`
`
`impinging jet is marked by an arrow. An important
`
`
`
`
`
`
`
`
`observation is that the heat transfer enhancement may
`
`
`
`
`
`
`
`occur when f, is close to 1,, and the heat transfer
`
`
`
`
`
`
`
`
`
`
`reduction may happen when fc is close to _f,',/2. The
`
`
`
`
`
`
`
`
`causes of the heat transfer enhancement and reduction
`
`
`
`
`
`
`
`will be explored in the following sections.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`RELATIONSHIP BETWEEN FLOW STRUCTURES
`
`Vortical structures and their effects on heat transfer
`In order to understand the relationship between the
`
`
`
`
`
`
`
`
`flow structures and heat
`transfer,
`the smoke vis-
`
`
`
`
`
`
`
`
`ualization was performed. The smoke from a cigarette
`
`
`
`
`
`
`
`smoke generator was gently introduced through a 1
`
`
`
`
`
`
`
`
`mm diameter TYGON tube into the flow at the nozzle
`
`
`
`
`
`
`
`
`
`
`lip. A strobe light placed behind a glass target plate
`
`
`
`
`
`
`
`
`
`
`was used to illuminate the flow structures through a
`
`
`
`
`
`
`
`
`
`narrow slot. Four successive photos of Fig. 7 show
`
`
`
`
`
`
`
`
`
`the stable pairing process of the ring vortices at
`
`
`
`
`
`
`
`
`
`f; = 950 Hz when H/D = 1.125 and Rer, = 12300,
`
`
`
`
`
`
`
`
`
`
`which corresponds to the case of the heat transfer
`
`
`
`
`
`
`
`
`
`reduction. The shear layer starts to roll up to form the
`
`
`
`
`
`
`
`
`
`
`
`discrete vortices before it impinges on the plate wall.
`
`
`
`
`
`
`
`
`
`Then, the vortices move in the radial direction along
`
`
`
`
`
`
`
`
`
`the wall. Because the excitation frequency fc is close
`
`
`
`
`
`
`
`
`
`to the subharmonic of the natural frequency, two vor-
`
`
`
`
`
`
`
`
`
`tices merge to form a bigger and stronger vortex at
`
`
`
`
`
`
`
`
`
`
`r/D = 1.7. The coalescence of two vortices is similar
`
`
`
`
`
`
`
`
`
`to that in the free jet, except that the trajectories of
`
`
`
`
`
`
`
`
`
`
`
`the vortices are deflected by the plate. After the vortex
`
`
`
`
`
`
`
`
`
`
`pairing, the resulting strong vortex in the outer shear
`
`
`
`
`
`
`
`
`
`layer induces a counter-rotating secondary vortex
`
`
`
`
`
`
`from the boundary layer at
`r/D = l.8—2.0. The
`
`
`
`
`
`
`
`
`
`appearance of the secondary vortex can be identified
`
`
`
`
`
`
`
`
`in photos 1 and 4 of Fig. 7. The secondary vortices
`
`
`
`
`
`
`
`
`
`
`
`induced by the large-scale vortices
`in a round
`
`
`
`
`
`
`
`
`impinging jet have been observed by Popiel and Trass
`
`
`
`
`
`
`
`
`
`[10]. This phenomena is also referred to the vortex-
`
`
`
`
`
`
`
`
`
`induced unsteady separation which is initiated by the
`
`
`
`
`
`
`
`
`unsteady adverse pressure gradient produced by the
`
`
`
`
`
`
`
`primary vortex [8]. The location of the vortex-induced
`
`
`
`
`
`
`
`
`unsteady separation coincides with the valley of the
`
`
`
`
`
`
`
`
`heat transfer distribution (r/D = 1.8—2.0) at _/"Q = 950
`
`
`
`
`
`
`
`
`
`Hz in Fig. 5. This suggests that the vortex-induced
`
`
`
`
`
`
`
`
`
`unsteady separation may induce the local heat transfer
`
`
`
`
`
`
`
`
`reduction. A significant decrease in heat transfer rate
`
`
`
`
`
`
`
`
`was also found by Rivir er al.
`[29]
`in a region of
`
`
`
`
`
`
`
`
`
`
`turbulent separation induced by an adverse pressure
`
`
`
`
`
`
`
`gradient on a Hat surface.
`
`
`
`
`In contrast with the case of]; = 950 Hz, the 1750
`
`
`
`
`
`
`
`
`
`
`
`Hz excitation produces ‘intermittent’ vortex pairing
`
`
`
`
`
`
`rather than the stable vortex pairing, as shown in Fig.
`
`
`
`
`
`
`
`
`
`
`8(a). The video tape indicates that the vortices jitter
`
`
`
`
`
`
`
`
`
`in space during the intermittent vortex pairing
`
`
`
`
`
`
`
`although thejittering cannot be seen in a single frame
`
`
`
`
`
`
`
`
`
`of the photo in Fig. 8(a). In this case, the time trace
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 5 of 12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`T. LIU and J. P. SULLIVAN
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Fig. 4. Two-dimensional Nusselt number distributions of excited impinging jet when H/D = 1.125 and
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Re” = 12300: (a)/'. — 950 Hz, (b)_/;. = 1750 Hz, (c) unexcited.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`of the hot-film signal shows that the subharmonic
`
`
`
`
`
`
`
`
`wave occurs intermittently. Also. the phase difference
`
`
`
`
`
`
`
`between the excited fundamental and self-generated
`
`
`
`
`
`
`subharmonic waves randomly drifts. Instead ofa well-
`
`
`
`
`
`
`
`organized vortex,
`the intermittent vortex pairing
`
`
`
`
`
`
`forms a chaotic ‘lump eddy‘ which contains a great
`
`
`
`
`
`
`
`
`
`
`deal of small-scale random turbulence (the term ‘eddy‘
`
`
`
`
`
`
`
`
`is used instead of ‘vortcx“ since the flow structure is
`
`
`
`
`
`
`
`
`
`
`not well-organized). The vortical structures become
`
`
`
`
`
`
`less organized after the intermittent vortex pairing. In
`
`
`
`
`
`
`
`
`this case. the flow Visualization does not show obvious
`
`
`
`
`
`
`
`
`
`vortex-induced separation. The location of the chaotic
`
`
`
`
`
`
`
`
`Page 6 of 12
`
`
`
`
`
`
`
`
`
`
`Unexcited
`
`———- f_ = 950 Hz
`...... .. f‘ = 1750 Hz
`
`
`
`Excited circular impinging jet
`
`
`
`
`
`
`
`
`)1
`
`
`
`
`
`
`
`Fig. 5. Transverse Nusselt number distributions of excited
`
`
`
`
`
`
`
`impinging jet when H/D = 1.125 and Rep = 12 300.
`
`
`
`
`
`
`
`
`
`
`2
`
`
`
`
`
`11
`
`0.15
`0.10
`0.05
`0.00
`-0.05
`-0.10
`0.10
`0.05
`
`T‘ 0.00
`
`
`
`0.0 0.5
`
`1.0
`
`1.5
`
`2.0 2.5 3.0
`
`3.5
`
`ip/U0
`Fig. 6. Heat transfer enhancement factor as a function of
`
`
`
`
`
`
`
`
`
`excitation frequency at r/D = 1.53 when R2,) = 12 300.
`
`
`
`
`
`
`
`
`
`
`
`
`‘lump eddy’ just corresponds to the second peak of the
`
`
`
`
`
`
`
`
`
`
`heat transfer distribution (r/D = 1.5-1.8) at f, : 1750
`
`
`
`
`
`
`
`
`Hz in Fig. 5. This suggests that an increase in the
`
`
`
`
`
`
`
`
`
`
`
`random turbulence causes the heat transfer enhance-
`
`
`
`
`
`
`
`ment. A similar observation has been reported by
`
`
`
`
`
`
`
`
`Kataoka et al. [12]. They found that the turbulent,
`
`
`
`
`
`
`
`less coherent structure can enhance the stagnation-
`
`
`
`
`
`
`
`point heat transfer more eflectively than the non-
`
`
`
`
`
`
`
`
`turbulent coherent structure with the periodic flue-
`
`
`
`
`
`
`
`tuation. For
`the
`unexcited
`impinging jet
`at
`
`
`
`
`
`
`
`
`no 0.,“
`
`
`3
`
`)
`
`
`
`
`
`
`
`
`2.5
`1.5
`0.5
`
`
`
`
`Fig. 7. Successive photos of stable vortex pairing in excited
`
`
`
`
`
`
`
`
`
`
`impinging jet at f, = 950 Hz when H/D = 1.125 and
`
`
`
`
`
`
`
`
`
`R2,, = 12 300.
`
`
`
`
`
`
`
`
`H/ D = 1.125, the organized vortices are shown in Fig.
`
`
`
`
`
`
`
`
`8(b). No vortex pairing is observed in this case.
`
`
`
`
`
`
`
`
`
`It is desirable to discuss effects of the large-scale
`
`
`
`
`
`
`
`
`
`organized vortices and small-scale random turbulence
`
`
`
`
`
`
`transfer in the wall—jet region. The heat
`on heat
`
`
`
`
`
`
`
`
`
`flux Q is expressed as a sum of
`three terms
`
`
`
`
`
`
`
`
`
`
`
`
`Q = —kéf/6y+pcPv;T;+pcpv{c7TC, where the sub-
`
`
`
`scripts c and ic represent the coherent component
`
`
`
`
`
`
`
`
`induced by the organized vortices and incoherent
`
`
`
`
`
`
`
`component caused by the small-scale random tur-
`
`
`
`
`
`
`
`bulence, respectively. The first term in the right-hand
`
`
`
`
`
`
`
`
`side is the mean heat flux, the second term represents
`
`
`
`
`
`
`
`
`
`
`the coherent part of the turbulent heat flux, and the
`
`
`
`
`
`
`
`
`
`
`third term denotes the incoherent part of the turbulent
`
`
`
`
`
`
`
`
`
`heat flux. It should be emphasized that the first term
`
`
`
`
`
`
`
`
`
`
`- k8 T"/6y is implicitly dependent on the coherent and
`
`
`
`
`
`
`
`random fluctuating velocities, because these flue-
`
`
`
`
`
`
`tuations modify the mean flow. For a hot wall, large-
`
`
`
`
`
`
`
`
`
`
`
`Page 7 of 12
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`T, LIU and J. P. SULLIVAN
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`from separation. but also significantly increases the
`incoherent heat flux {)(‘pl.‘;cT,/C. Overall, the local heat
`
`
`
`
`
`
`
`transfer is enhanced in this case.
`
`
`
`
`
`
`
`Heat‘ transfer spectra
`The dynamic aspects of the impinging jet can be
`
`
`
`
`
`
`
`
`
`further studied by examining spectra of the time-
`
`
`
`
`
`
`
`
`dependent heat transfer fluctuation. The local heat
`
`
`
`
`
`
`
`transfer fluctuation was measured by a flush—mount
`
`
`
`
`
`
`
`hot-film sensor. The spectrum development of the
`
`
`
`
`
`
`
`relative heat transfer fluctuation Q"/QI, at different
`
`
`
`
`
`
`radial locations on the wall is shown in Fig. 9(a) for
`
`
`
`
`
`
`
`
`
`
`
`the case of]; : 950 Hz and H10 2 L125 (heat trans-
`
`
`
`
`
`
`
`
`
`
`fer reduction case). where Q‘, is the mean heat transfer
`
`
`
`
`
`
`
`
`
`
`rate at the stagnation—point. For comparison. the cor-
`
`
`
`
`
`
`
`
`responding heat
`transfer spectra of the unexcited
`
`
`
`
`
`
`
`impinging jet are also plotted. In all spectra for the
`
`
`
`
`
`
`
`
`
`
`excited impingingjet the excitation frequency]; com-
`
`
`
`
`
`
`
`
`ponent is dominant. although the harmonics and weak
`
`
`
`
`
`
`
`
`randomness are present. Since /Q. is close to the sub-
`
`
`
`
`
`
`
`
`
`harmonic of the natural frequency, the excitation pro-
`
`
`
`
`
`
`
`
`motes vortex pairing as indicated by the flow vis-
`
`
`
`
`
`
`
`
`
`ualization. Compared with the unexcited case. the 950
`
`
`
`
`
`
`
`
`Hz excitation considerably suppresses the broad spec-
`
`
`
`
`
`
`
`tral components ofthe small-scale random turbulence
`
`
`
`
`
`
`
`such that the well-defined characteristic frequencies f“
`
`
`
`
`
`
`is still distinguishable at r/D : 1.85. This is consistent
`
`
`
`
`
`
`
`
`with the flow visualization observation which indi-
`
`
`
`
`
`
`
`cates the existence of the well—organized vortices at
`
`
`
`
`
`
`
`
`r,'[) = 1.8 after stable pairing. Figure l0(a) shows the
`
`
`
`
`
`
`
`
`
`spatial evolution of two dominant modes _f; and 2];
`
`
`
`
`
`
`
`
`along the radial direction. The amplitudes of the 1;.
`
`
`
`
`
`
`
`
`
`and 2]; modes grow exponentially at the beginning.
`
`
`
`
`
`
`
`
`reach a maximum at r/D : l and then decay. The
`
`
`
`
`
`
`
`
`
`
`fluctuation intensity that
`includes the con-
`total
`
`
`
`
`
`
`
`tributions from all spectral components is also given
`
`
`
`
`
`
`
`
`for comparison. The amplitude difference between the
`
`
`
`
`
`
`
`total
`intensity and discrete modes represents the
`
`
`
`
`
`
`
`amount of randomness. Figure l0(a) indicates that
`
`
`
`
`
`
`
`the f_. mode is so dominant that the flow is highly
`
`
`
`
`
`
`
`
`
`
`
`coherent for r,/D : 0.5-1.0. Only after r/D 2 1.5. do
`
`
`
`
`
`
`
`the broad spectral components of the small-scale ran-
`
`
`
`
`
`
`
`
`dom turbulence beeome evident. The heat transfer
`
`
`
`
`
`
`
`reduction occurs after the dominant modes saturate.
`
`
`
`
`
`
`
`Note that thef; spectral component has a local mini-
`
`
`
`
`
`
`
`
`
`mum at r/D 2 1.75 where the greatest heat transfer
`
`
`
`
`
`
`
`
`reduction is attained. From the flow visualization
`
`
`
`
`
`
`
`photos in Fig. 7, it can be found that the location of
`
`
`
`
`
`
`
`
`
`
`
`
`the amplitude minimum at r/‘D = 1.75 corresponds to
`
`
`
`
`
`
`
`
`the separation point between the primary vortex and
`
`
`
`
`
`
`
`
`secondary vortex. The
`secondary
`induced
`the
`
`
`
`
`
`
`maximum of the]; spectral component at r/D = 2 is
`
`
`
`
`
`
`
`
`caused by the generation ofthe secondary vortex. The
`
`
`
`
`
`
`
`
`
`spectral analysis supports the observation that the
`
`
`
`
`
`
`
`vortex-induced separation causes the local heat trans-
`
`
`
`
`
`
`
`fer reduction.
`
`
`transfer enhancement
`When /L. = 1750 Hz (heat
`
`
`
`
`
`
`
`
`the subharmonic component fa"/2 is spon-
`case).
`
`
`
`
`
`
`taneously generated and has a comparable amplitude
`
`
`
`
`
`
`
`to the excited fundamental mode 1; Over a range of
`
`
`
`
`
`
`
`
`
`
`
`
`
`0.5
`r/D
`2.5
`1.5
`Fig. 8. Vertical structures ofimpingingjet when H/D : 1.125
`
`
`
`
`
`
`
`
`
`
`and Rep = 12300: (a)_fi : 1750 Hz. (b) unexcited.
`
`
`
`
`
`
`
`
`
`
`
`
`
`scale