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Influence of shear layer dynamics on impingement heat transfer
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Influence of Shear Layer Dynamics on Impingement Heat Transfer Carosena Meola Luigi de Luca Giovanni M. Carlomagno Universit~ degli Studi di Napoli "Federico II," Dipartimento di Energetica, Termofluidodinamica Applicata e Condizionamenti Ambientali (DETEC), Naples, Italy
• Measurements of convective heat transfer coefficients on a flat plate with an air jet impinging on it perpendicularly are made to investigate the influence of some governing parameters. Particular attention is focused on the effects of the shear layer dynamics. For certain flow conditions and/or test arrangements, coherent structures and/or recirculation currents are observed affecting the distribution of the heat transfer coefficients. Measurements of wall temperature as well as of adiabatic wall temperature of the stream are made by means of an infrared scanning radiometer, and the heat transfer coefficients are calculated by means of the so-called heated thin foil technique. The data are reduced in dimensionless form as Nusselt numbers and compared with data from the available literature. Both spatial distributions and averaged values of the Nusselt number are discussed. A new explanation for the second peak in the local Nusselt number is proposed. Keywords: impingement heat transfer, recirculation currents, jet instability, infrared thermography
INTRODUCTION Jets of fluids have been and are still of great interest because of their wide industrial applications. In fact, jets are used to dissipate heat generated by microelectronic circuits, to cool the leading edge of turbine blades, to heat the zones critical for the formation of ice over aircraft, to dry textiles, and to temper glass. Earliest measurements of heat transfer of an air jet impinging on a flat plate were done by Gardon and Cobonpue [1], who considered the influence of nozzle exit diameter, nozzle-to-plate distance, and flow rate (Reynolds number). Later, Gardon and Akfirat [2] accounted for the role of turbulence in heat transfer measurements. Many studies have been made involving jets with and without the same temperature as the ambient fluid, and effects of thermal entrainment have been investigated. In this context, Striegl and Diller [3, 4] developed an analytical model for the case of a single turbulent plane jet. Goldstein et al. [5] carried out experimental studies of recovery factor and local heat transfer for an axisymmetric impinging air jet. Hollworth and Wilson [6] characterized a heated turbulent air jet and performed measurements of mean axial velocity and total temperature in the jet as well as recovery temperature on a fiat surface normal to the jet axis. It is worth noting that heat transfer levels reported by Gardon and Cobonpue [1] and Hollworth and Gero [7] seem to be higher than those shown by Goldstein and
coworkers [5, 8, 9] for short radial distances. Also, Nusselt number values reported in a recent paper by Mohanty and Tawfek [10] are surprisingly higher compared to those in the current literature, in particular the work of Baughn et al. [11, 12]. Discrepancies may be associated with the jet displacement after impingement, which is linked in part to the nozzle shape and in part to the jet-and-plate arrangement. It should be noted that the works reported in the literature include various values of the governing parameters such as the nozzle shape, the outlet diameter, the nozzle length, the position of the nozzle with respect to the plate, and so forth. In addition, some studies are lacking in fundamental information, making generalization of experimental results difficult, As stated recently in the review paper of Viskanta [13], there is considerable discrepancy between the correlations for the average Nusselt number that have been proposed by various workers with respect to the dependence on Reynolds number, spacing ratio, and averaging area. In this context, the way in which Sparrow and Lowell [14] presented results (i.e., recasting data in terms of radial decay) overcomes the drawbacks due to the different test conditions employed by the different investigators and makes a general comparison possible. To our knowledge, the external factors linked to the jet-and-plate arrangement have not been considered adequately. The flat plate is generally considered an open surface; but then, the recirculation currents present in an enclosed surface [15, 16] can still exist when the jet
Address correspondence to Dr. Carosena Meola, Universit~ di Napoli--DETEC, P. le Tecchio, 80, 80125 Naples, Italy.
Experimental Thermaland Fluid Science 1996; 13:29-37 © Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010
0894-1777/96/$15.00 PII S0894-1777(96)00011-8
30
Carosena Meola et al.
impinges on a flat plate if there is not sufficient room for the air jet, after impingement, to flow freely toward the ambient. These effects might represent a potential error source leading to contradictory results when the experimental data of different workers are compared. Another aspect to be considered is the occurrence of some jet instabilities observed at certain flow conditions that alter the distribution of the wall temperature with loss of circumferential appearance (for a round nozzle) and the formation of azimuthal structures. Jet instability has been generally analyzed from the point of view of pressure and velocity fluctuations for a self-excited jet [17] or an acoustically forced jet [18]. Recently, Meola et al. [19] recognized the importance of the entrainment effects (which entail fluctuations of pressure and temperature) on the onset of the instability process. Popiel and Trass [20] observed ring-shaped wall eddies using a smoke-wire visualization technique and suggested that these wall eddies could be responsible for the additional enhancement of local momentum and heat or mass transfer and for the second peak in local Nusselt number. Lytle and Webb [21] instead speculated that the outer peak in the Nusselt number was a result of a transition from laminar to turbulent flow in the boundary layer. More details about the disagreement concerning the formation of the outer peak can be found in Viskanta's review [13]. The intention of the present experimental study is to ascertain the presence of the recirculation currents on an open surface when a circular jet impinges on it. The influence of such recirculation currents and of the instability structures on the heat transfer coefficients and particularly on the formation and location of the outer peak is investigated. EXPERIMENTAL SETUP AND TECHNIQUE The experimental apparatus is sketched in Fig. 1. The impingement plate is a thin constantan foil (200 mm wide, 470 mm long, and 0.050 mm thick) held flat by a stiffening fixture. The foil is heated by passing an electric current through it and cooled by an air jet directed perpendicular to it. The electric current is provided with a direct current power supply within 1% uncertainty. The cooling air jet, supplied by a compressor, goes through a pressureregulating valve, a heat exchanger, then, after filtering, to a plenum chamber where pressure and temperature are metered, and then flows through a replaceable nozzle. The nozzle is a truncated cone manufactured with three exit diameters D of 3, 5, and 10 mm, respectively, and
with length L = 50 mm for D = 3 5 mm and L = 100 mm for D = 10 mm. The dimensionless nozzle-to-plate distance Z/D ranges from 2 up to 100, 70, and 30 for the three nozzle diameters. The Mach number M ranges from 0.04 to 0.78 and the Reynolds number Re = V D / v from 10,000 to 173,000; both M and Re are based on the nozzle exit velocity V. In the specific test arrangement (Fig. 1), the nozzle is supported by a flange that is the end of the stagnation chamber. To assess if and how the flange may influence the heat transfer distribution, two stagnation chambers of external diameters 130 and 110 mm are used with supporting nozzle flanges of external diameters 260 and 110 mm, respectively. These chambers are referred to here simply as chamber A and chamber B. A computerized infrared scanning radiometer (IRSR), based on an A G E M A Thermovision 880LW scanner connected via a TIC 8000 A / D converter board to an IBM computer, is employed to measure surface temperatures. The object radiation is detected by means of a mercury cadmium telluride (MCT) element covering the 8-12 /zm band. Nominal sensitivity, expressed in terms of N E T D (noise equivalent temperature difference) is 0.07°C when the scanned object is at ambient temperature. IRSR is applied to the heated thin foil technique, which consists in measuring the convective heat transfer coefficient h between a very thin metallic foil heated by the Joule effect and the air jet impinging on it. The surface temperature distribution is measured by viewing the rear face of the foil, that is, the opposite side of jet impingement. In fact, since the Biot number Bi = hs/kf (where s and kf are the thickness and thermal conductivity of the foil, respectively) is much less than unity (in the present tests Bi ranges from 1.56 × 10 _4 to 5.46 × 10 3), the temperature can be considered practically uniform across the foil thickness. So h is evaluated as
h
Q
Tw- Lw'
where Q is the Joule heating per unit area (corrected for lateral conduction within the foil, radiation, and natural convection losses when not negligible), and Tw and Taw are wall temperature and adiabatic wall temperature of the stream. Each test run consists of two parts. First, with electric current off, the foil surface temperature is assumed to coincide with Taw and the "cold image" is recorded. Second, electric current on, Tw is displayed and the "hot
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Impingement Heat Transfer 31 image" is recorded. In particular, each image is obtained by averaging 16 images in time sequence. The high sensitivity of IRSR allows keeping Joule heating quite low (450-4800 W / m 2, depending on Re and M values), avoiding high foil temperature. As a result, the electrical resistivity of the foil can be assumed constant. For the employed values of Joule heating, the uncertainty of the absolute temperature measurement is approximately 0.1% of its value. A lens of 7° is used with spatial resolution, at minimum focus distance, of 1 pixel/mm; for better visualization of the formation of instability structures the resolution is increased (to about 3 pixels/mm) by means of an extension ring. The surface of the foil viewed by IRSR is coated with a thin film of black opaque paint with emissivity factor e equal to 0.95. The emissivity factor has been measured, still by the IR system, by relating the detected radiation from a specimen heated by means of a bath/circulator with its actual temperature measured by means of a mercury thermometer. To quantify the influence of the relative position of the jet with respect to the plate, a different arrangement is used, with the plate horizontal and the jet impinging upward. In this case, since it is not possible to maintain the IR scanner with its roll axis in the vertical position (the dewar chamber for the liquid nitrogen cooling the IR detector cannot stand an inclination angle greater than 70°), the image is reflected from a mirror placed at 45 °. To minimize undesired reflection from the surroundings, the entire test apparatus is put in a darkroom while mirror absorption and other eventual radiation losses are taken into account by calibration, by means of a blackbody source, of the thermographic system for the actual test conditions. In the particular application, owing to the necessity of taking experimental readings with high spatial resolution and of detecting the transient circumferential movement of the azimuthal structures, infrared thermography acted as a very effective tool because of its high sensitivity, nonintrusive character, and two-dimensionality [22]. Data presented hereafter do not generally need any correction in the way of image restoration [23]. Furthermore, because of the small temperature differences encountered in the measurement of the adiabatic wall temperature, it is not corrected for radiation and radial conduction. The evaluation of the convective heat transfer coefficient h, instead, needs to take into account both radiation and conduction corrections [24]. So Equation (1) has to be rewritten as
Qh=
-kfs ~
+ ~ O---R- + e~r(T~- TJ) Tw - Taw
(2) where tr is the Stefan-Boltzman constant. Differences between corrected and uncorrected data are generally on the order of 2-6%. H E A T T R A N S F E R MEASUREMENTS Hereafter, heat transfer data, generally averaged over each circumference of given radius R/D, are reduced in
dimensionless form in terms of Nusselt number Nu defined as Nu = hD/k,
(3)
where k is the thermal conductivity of air evaluated at the film temperature and h is calculated from Eq. (2). The Nusselt number is evaluated within an uncertainty of 4-10%.
Influence of the Jet-and-Plate Arrangement Some tests are carried out by employing the experimental arrangement of Fig. 1 (i.e., vertical plate) with chamber A (with a large flange). In such a configuration, a lowpressure zone in the corner where the nozzle is joined to the flange may develop as the jet issues from the nozzle. This, in the case of a short flange-to-plate distance Dp, promotes recirculation currents with flow separation over the plate. At low Reynolds numbers and obviously when the plate is heated, buoyancy effects can originate in the wall jet region (at relatively high R/D values) and can cause a time increase of the jet temperature with consequent time-dependent heat transfer decreasing. This occurrence, in particular, is stressed as the Joule heating is increased. In the present work, buoyancy effects are investigated by means of the schlieren technique and by means of the same IR imaging system by viewing the lateral side of the nozzle. The reversal flow is seen to cross the nozzle or the jet flow (depending on Z/D) at a distance of 30 mm from the plate. Next, a new series of tests are carried out by considering a modified experimental apparatus with the plate positioned horizontally and the jet impinging upward. Different D~ values (35-220 ram) for a fixed Z / D are considered t~at are obtained by lengthening the nozzle with straight ducts of internal diameter equal to the nozzle entrance diameter and of different lengths. The presence of recirculation effects is investigated by following the deflection of a small tuft and by means of the schlieren technique. Two pictures for (a) closed and (b) open impingement surface are shown in Fig. 2. Owing to the difficulty of taking a well-resolved picture from the schlieren image (the streak lines do not have sufficient contrast), two small tufts were glued to opposite sides of the nozzle lip; the flow field can be interpreted from the deflection of such tufts. When a large flange is positioned close to the plate (low Dp values), the jet air, after impingement, is not able to flow freely toward the ambient and comes back to the flange (Fig. 2a). Separation (over the target plate) occurs at about 1.2D from the jet center where, as stated by Martin [25], the vertical component of the jet velocity is decelerated and transformed into a horizontal component. These points of flow separation are generally (also in an open case) present in the jet flow field at short impingement distances and coincide quite well with the location of the well-known vortex rings; in an open case, the flow reattaches downstream at about 2D (depending on the Reynolds number) and follows the surface of the target plate, slightly diverging far away. Separation and reattachment of the jet flow give rise, in terms of heat transfer, to the minimum in the Nusselt number distribution at about 1.2D and to the maximum
32
Carosena Meola et al.
at about 2D; the presence of such minima and maxima in the Nusselt number distribution is widely documented [1, 11-13, 21]. On the other hand, for low Dp values or better, when the flange, as in Fig. 2a, is too close to the target plate, the jet flow, because of the aforementioned low-pressure zone at the nozzle-to-flange junction, is prevented from reattaching and is transformed into recirculation patterns. The essential fact underlying the flow behavior is that the recirculation effects are in contrast to the formation of the outer (second) peak in the local Nusselt number. As Dp is increased, the recirculation tends to vanish and the air jet flows follow the target plate
surface as shown in Fig. 2b. As a consequence, there is local increase in heat transfer, and the lateral peaks in the Nusselt number distribution become more pronounced. At last, the measurements of heat transfer (for the same flow conditions relative to the test arrangements mentioned above) are repeated on an impingement surface made more open by employing the slender chamber B. No recirculation patterns are now observed, and this configuration is assumed to be ideal. The Nusselt number distributions for the different jetand-plate arrangements are shown in Fig. 3 for a truncated cone nozzle of D = 5 mm, Z / D = 2, and Re =
Ca )
(b)
Figure 2. Flow visualization. (a) Closed impingement surface; (b) open impingement surface.
Impingement Heat Transfer 33 50,000. It is evident from the Nusselt number distributions that the test arrangement (with regard to the dimensions of the stagnation chamber), at short impingement distances, drives the flow displacement. In particular, the Nusselt number distribution for the slender chamber B matches quite well the distribution relative to higher D o values for chamber A, indicating that both cases are free of recirculation effects. The Nusselt number distributions for D = 10 mm, Re = 60,000, and several Z / D values, obtained by employing the final ideal experimental setup (horizontal plate and slender stagnation chamber B) without recirculation effects, are shown in Fig. 4. These radial Nu distributions follow the well-known description given by Gardon and Cobonpue [1].
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The heat transfer to an impinging jet is governed by flow conditions that are usually summarized by the Reynolds number, the Mach number, and the jet total temperature. The influence of the Reynolds number on the Nusselt number distribution has already been analyzed by previous workers and will not be considered here. As regards the influence of the Mach number, it has been found that when the jet impinges within its potential core at the critical value of the Mach number M = 0.7, the vortex rings break up, giving rise to the formation of azimuthal structures [19]. The presence of such structures can be evidenced through the maps of Taw and Tw reported in Fig. 5, which refers to D = 5 mm, Z / D = 4, and M = 0.78 (Re = 86,400). It is worth noting that data presented in the following text refer, unless otherwise specified, to the final experimental setup (horizontal plate and slender stagnation chamber B), which does not include the undesired effects such as buoyancy and recirculation. As can be seen in Figs 5a and 5b, both t~mperature distributions, Taw and T w, are affected by the jet instability, and the temperature fluctuations are of the same order in both cases. This finding is better shown in Figs. 6 and 7, where the circumferential averages of Taw and Tw are reported for various Mach numbers. Note that
200
250
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4. Nusselt number radial distributions for various nozzle-to-plate distances. Figure
the distributions of Taw and Tw depend strongly on the Mach number. For M < 0.7 a minimum is present at R / D ~ 1.2; when the Mach number reaches the value of 0.7, this minimum is split into two minima separated by a relative maximum. Since the temperature fluctuations at M > 0.7 for Taw and Tw are of the same order of magnitude, the radial distribution of the Nusselt number, averaged along circumferential patterns, does not show additional peaks as can be seen in Fig. 8. Nevertheless, some azimuthal structures are visible in the two-dimensional map of the Nusselt number (Fig 5c). In addition, the local Nusselt number contours (Fig. 5c) exhibit loss of symmetry about the stagnation point, this effect being due to the transient alternate circumferential movement of the instability structures [19]. By contrast, for low Mach numbers and therefore low Reynolds numbers (e.g., M = 0.3 and Re = 34,000, as shown in Fig. 5d), the flow is not affected by instability, and the Nusselt number contours display circumferential symmetry. Outside the potential core region, the instability starts at a lower Mach number; for instance, at Z / D = 6 the presence of the secondary minima can be noticed already at M = 0.41 because of the mixing, which enters the potential core, entailing entrainment of warmer ambient air. Since the organization of the instability structures is governed by the entrainment of ambient air in the shear layer [19], the test arrangement is of utmost importance. In the case of a close impingement surface, the ambient air is prevented from interfering with the jet while recirculation currents originate at the separation point. As a consequence, the formation of the instability structures is contrasted. The data considered so far refer to the total jet temperature TO close to the ambient temperature Ta. The temperature difference between TO and Ta drives the entrainment and affects the Nusselt number distribution. In this way, from preceding arguments in this paper, it is clear that the dependency on the temperature difference has to be considered within the specific test arrangement. In particular, a hot air jet impinging on a vertical plate displays upward movement of the stagnation point, split-
34
Carosena Meola et al. ,
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ting it into two contiguous stagnation points. This effect is not evident when the jet impinges upward on a horizontal plate, in which case rotation of the w a r m e r jet air surr o u n d e d by the cold ambient air is observed. Obviously, the flow dynamics d e p e n d on the impingement surface configuration, open or closed. M o r e a p p r o p r i a t e investigations into the flow behavior with variation of the thermal boundary conditions are still under way. However, it is well known that the potential core tends to shorten as the jet t e m p e r a t u r e increases. As shown in Fig. 9, which refers to impingement on a horizontal plate, the outer Nu peaks relative to Z / D = 4 for To - Ta = 4 0 ° C b e c o m e much milder and Nu values around the stagnation point increase, to approach the distribution relative to Z / D = 6 for T0 - Ta = 0 ° C .
DISCUSSIONS AND DATA CORRELATIONS In light of the available literature and the present results, there is some evidence to support the hypothesis [20] that the vortex rings could be responsible for the formation of the second p e a k in the local Nusselt number. The vortex rings, for M < 0.7 [19], keep their structure after impingment, as the annular minima present in the temperature distribution of Figs. 6 and 7 show. A vortex ring acts as an obstacle in the free stream and causes separation and turbulent reattachment downstream. The reattachment point coincides with the maximum in heat transfer, and its location depends on the magnitude of the vortex rings. As the Mach number increases (the vortex ring stretches), the p e a k moves downstream, as was also observed by Lytle
Impingement Heat Transfer 400
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mal boundary conditions. It must be remarked that the recirculation currents oppose the flow reattachment and the formation of the outer peak (Fig. 3). Finally, the effects of the jet instability and the recirculation currents on the average Nusselt number are investigated. Data are averaged over a circular area of radius 6 times the nozzle diameter. First, only data relative to an ideal experimental apparatus without the two phenomena mentioned above are considered. Following the empirical correlations proposed by Klammer and Schupe and reviewed by Viskanta [13], it is found that the Nusselt number depends on the Reynolds number to the 0.65 power, and this is in general agreement with Martin [25]. Values of N u / R e °65 are plotted against Z / D in Fig. 10 for the three nozzle diameters, R / D = 6, and 10,000 < Re < 100,000. As can be seen, the average Nusselt number is independent of Z / D for Z/D < 10, while the correlation curve for Z/D > 10 is Nu = 0.548
Re°65(Z/D)-0714.
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(4)
To - Ta = 40 *C Z/D=4
To=Ta
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-2
Figure 8. Influence of Mach number on Nu radial distribution.
200
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and Webb [21]. At a Mach number of 0.7 the vortex rings break up upon impact with the wall, leading to entrainment of warmer ambient air. As a consequence, two minima with a maximum between them are formed (Figs. 6 and 7) that are associated with the splitting of the primary vortex ring into two secondary vortex rings. The peak in the Nusselt number, as shown in Fig. 8, moves upstream, following the location of the first vortex ring, which is now closer to the jet center. It is worth noting that the distributions shown in Fig. 8 are obtained by averaging data over circumferences of given radius; conversely, after breakup, azimuthal structures are formed (Fig. 5c) and the outer peak assumes different values from point to point over the same circumference. The radial position of the outer peak moves toward the jet center as the impingement distance is reduced [21], and that is linked to the variation of the location of the primary vortex ring with the impingement distance [19]. On the other hand, the jet displacement after impingement is governed by the test arrangement as well as by the ther-
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Figure 9. Influence of the jet total temperature.
6
36
Carosena Meola et al.
a
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°: iiiiiiiii t ,Re o
10 mm (Re = 1 0 0 0 0 - 1 0 0 0 0 0 )
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Figure 10. Correlation for the average Nu number.
In addition to jet instability effects, it has already been observed that the Nusselt number is affected only locally (Fig. 5c) by the azimuthal structures. The spatial distributions obtained by averaging the Nu values along circumferential patterns are quantitatively analogous to the ones for the ideal case (Fig. 8), and similar behavior is, of course, found for the average values over a circular area. The recirculation currents instead have strong effects on the average Nusselt values and can cause a decrease of 20% at the shorter impingement distances. The recirculation currents, in fact, favor the flow separation and contrast the reattachment. As a consequence, the lateral peaks are destroyed with a smooth decrease in the Nusselt number distribution, which now takes the form of a bell shape. A comparison of the three correlation curves relative to the three cases--ideal, with instability, and with recirculation--is shown in Fig. 11. PRACTICAL SIGNIFICANCE/USEFULNESS Fluid jets are of great interest because of their wide industrial applications. In fact, jets are used to dissipate
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Figure 11. Influence of instability and recirculation currents on the average Nusselt number.
heat generated by microelectronic circuits, to cool the leading edge of turbine blades, to heat the zones critical to the formation of ice over aircraft, to dry textiles, and to temper glass. The external factors linked to the jet-andplate arrangement have not been considered adequately before. The fiat plate is generally considered an open surface; but then, the recirculation currents present in an enclosed surface can still exist when the jet impinges on a fiat plate if there is not sufficient room for the air jet, after impingement, to flow freely toward the ambient. The present experimental study on impingement heat transfer focuses attention on some phenomena induced in the shear layer by flow conditions and impingement setup. From a practical standpoint, the phenomena of recirculation currents and azimuthal structures arising in the local flow field are of great importance in obtaining results that can be used for different applications. Both of the effects mentioned above may result in undesired temperature distributions over the surface under treatment and can pose a serious problem in practical applications where precise standards are required. In particular, the recirculation currents induce a decrease of about 20% (at short impingement distances) in the average Nusselt number with respect to the ideal case.
CONCLUSIONS An experimental investigation into convective heat transfer coefficients between a flat plate and a round air jet impinging on it has been made in an attempt to assess the dependency of the second peak in the Nusselt number on shear layer dynamics. The critical difference in opinion [20, 21] as to how the outer peak is achieved, evidenced by Viskanta in his review [13], has been analyzed accurately. As the major conclusion of the present work (on account of the high spatial resolution of infrared thermography), there is experimental evidence to argue that the vortex rings are responsible for the second Nu peak as was speculated by Popiel and Trass [20]. The formation and location of the outer peak may be considered a result of flow reattachment rather than a simple transition from laminar to turbulent. It has to be pointed out as a matter of particular importance that the jet-and-plate arrangement plays a key role in the flow displacement after impingement. Recirculation currents can exist also on a flat plate if there is not sufficient free room for the air jet to flow downstream and can interfere with the formation of the outer peak. From a practical standpoint, the phenomena (recirculation currents and azimuthal structures) arising in the local flow field are of great importance in obtaining results that can be used for different applications. Both of the effects mentioned above may result in undesired temperature distributions over the surface under treatment and might be a serious problem in practical applications where precise standards are required. The instability structures show only local effects; minima and maxima compensate each other when averaging data over circular areas. The strong effects of the recirculation currents instead remain after that average is obtained. In particular, the recirculation currents induce a decrease of about 20% (at short impingement distances) in the average Nusselt number with respect to the ideal case.
Impingement H e a t Transfer
NOMENCLATURE Bi D Dp h
Blot n u m b e r ( = h s / k O , d i m e n s i o n l e s s nozzle exit d i a m e t e r , m c h a m b e r f l a n g e - t o - p l a t e distance, m c o n v e c t i v e h e a t transfer coefficient [see Eq. (2) for definition], W / ( m 2- K) k t h e r m a l conductivity o f the air, W / ( m • K) kf t h e r m a l conductivity o f the foil, W / ( m • K) L n o z z l e length, m M Mach number, dimensionless N u local Nusselt n u m b e r ( = h D / k ) , d i m e n s i o n l e s s N u a v e r a g e Nusselt n u m b e r ( = h D / k ) , d i m e n s i o n l e s s Q J o u l e heating, W R radial distance f r o m j e t center, m R e jet R e y n o l d s n u m b e r ( = V D / v ) , d i m e n s i o n l e s s s foil thickness, m Za a m b i e n t t e m p e r a t u r e , K Taw adiabatic wall t e m p e r a t u r e , K Tw wall t e m p e r a t u r e , K V velocity at nozzle exit, m / s X, Y Z
spatial c o o r d i n a t e s (~/X 2 + y Z = R), m i m p i n g e m e n t distance, m G r e e k Symbols emissivity coefficient, d i m e n s i o n l e s s k i n e m a t i c viscosity o f the air, m 2 / s
Subscript 0
stagnation conditions REFERENCES
1. Gardon, R., and Cobonpue, J., Heat Transfer Between a Flat Plate and Jets of Air Impinging on It, Second Heat Transfer Conference, pp. 454-460, New York, 1962. 2. Gardon, R., and Akfirat, J. C., The Role of Turbulence in Determining the Heat-Transfer Characteristics of Impinging Jets, Int. J. Heat Mass Transfer 8, 1261-1272, 1965. 3. Striegl, S. A., and Diller, T. E., The Effect of Entrainment Temperature on Jet Impingement Heat Transfer, J. Heat Transfer 106, 27-33, 1984. 4. Striegl, S. A., and Diller, T. E., An Analysis of the Effect of Entrainment Temperature on Jet Impingement Heat Transfer, Trans. ASME 106, 804-810, 1984. 5. Goldstein, R. J., Behbahani, A. I., and Heppelmann, K. K., Streamwise Distribution of the Recovery Factor and the Local Heat Transfer Coefficient to an Impinging Circular Air Jet, Int. J. Heat Mass Transfer 29J, 1227-1235, 1986. 6. Hollworth, B. R., and Wilson, S. I., Entrainment Effects on Impingement Heat Transfer. Part 1. Measurements of Heated Jet Velocity and Temperature Distributions and Recovery Temperatures on Target Surface, ASME J. Heat Transfer 106, 797-803, 1984. 7. Hollworth, B. R., and Gero, L. R., Entrainment Effects of Impingement Heat Transfer. Part II. Local Heat Transfer Measurement, ASME Paper 84 WA/HT-20, 1984.
37
8. Goldstein, R. J., and Franchett, M. E., Heat Transfer from a Flat Surface to an Oblique Impinging Jet, Trans. ASME 110, 84-90, 1988. 9. Goldstein, R. J., Sobolik, K. A., and Seol, W. S., Effect of Entrainment on the Heat Transfer to a Heated Circular Air Jet Impinging on a Flat Surface, Trans. ASME 112, 608-611, 1990. 10. Mohanty, A. K., and Tawfek, A. A., Heat Transfer Due to a Round Jet Impinging Normal to a Flat Surface, Int. J. Heat Mass Transfer 36, 1639-1647, 1993. 11. Baughn, J. W., and Shimizu, S., Heat Transfer Measurements from a Surface with Uniform Heat Flux and an Impinging Jet, Trans. ASME J. Heat Transfer 111, 1096-1098, 1989. 12. Baughn, J. W., Hechanova, A. E., and Yan, X., An Experimental Study of Entrainment Effects on the Heat Transfer from a Flat Surface to a Heated Circular Impinging Jet, Trans. ASME J. Heat Transfer 113, 1023-1025, 1991. 13. Viskanta, R., Heat Transfer to Impinging Isothermal Gas and Flames Jets, Exp. Thermal Fluid Sci. 6, 111-134, 1993. 14. Sparrow, E. M., and Lovell, B. J., Heat Transfer Characteristics of an Obliquely Impinging Circular Jet, Trans. ASME J. Heat Transfer 102, 202-209, 1980. 15. Jusionis, V. J., Heat Transfer from Impinging Gas Jets on an Enclosed Concave Surface, Eng. Notes 7, 87-88, 1970. 16. Meo!a, C., no, G. M., Riegel, E., and Salvato, F., An Experimental Study of an Anti-Icing Hot Air Spray Tube System, 19th Cong. Int. Council Aeronaut. Sci., 3, 2345-2351, Anaheim, CA, 1994. 17. Donaldson, C. D., and Snedeker, R. S., A Study of Free Jet Impingement. Part I. Mean Properties of Free and Impinging Jets, J. Fluid Mech. 45, 281-319, 1971. 18. Didden, N., and Ho., C. M., Unsteady Separation in a Boundary Layer Produced by an Impinging Jet, J. Fluid Mech. 160, 235-256, 1985. 19. Meola, C., de Luca, L., and Carlomagno, G. M., Azimuthal Instability in an Impinging Jet: Adiabatic Wall Temperature Distribution, Exp. Fluids 18, 303-310, 1995. 20. Popiel, C. O., and Trass, O., Visualization of a Free and Impinging Round Jet, Exp. Thermal Fluid Sci. 253-264, 1991. 21. Lytle, D., and Webb. B. W., Secondary Heat Transfer Maxima for Air Jet Impingement at Low Nozzle-to-Plate Spacing, in Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, J. F. Keffer, R. K. Shah, and E. N. Ganic, Eds., pp. 776-783, Elsevier, New York, 1991. 22. Carlomagno, G. M., and de Luca, L., Infrared Thermography in Heat Transfer, in Handbook of Flow Visualization, W. J. Yang, Ed., pp. 531-553, Hemisphere, New York, 1989. 23. de Luca, L., Computerized IR Thermography for Convective Heat Transfer Measurements, in Computational Methods and Experimental Measurement, A. Sousa, C. A. Brebbia, and G. M. Carlomagno, Eds., pp. 347-358, CMP/Elsevier, New York, 1991. 24. de Luca, L., Cardone, G., and Carlomagno, G. M., Fluid Dynamics Applications of IR Imaging System, in Quantitative Infrared Thermography QIRT 92, D. Balageas, G. Busse, and G. M. Carlomagno, Eds., Editions Europeennes Thermique et Industrie, Paris, pp. 98-104, 1992. 25. Martin, H., Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces, Adv. Heat Transfer 13, 1-60, 1977.
Received October 10, 1995; revised February 7, 1996
,'
!
ELSEVIER
Influence of Shear Layer Dynamics on Impingement Heat Transfer Carosena Meola Luigi de Luca Giovanni M. Carlomagno Universit~ degli Studi di Napoli "Federico II," Dipartimento di Energetica, Termofluidodinamica Applicata e Condizionamenti Ambientali (DETEC), Naples, Italy
• Measurements of convective heat transfer coefficients on a flat plate with an air jet impinging on it perpendicularly are made to investigate the influence of some governing parameters. Particular attention is focused on the effects of the shear layer dynamics. For certain flow conditions and/or test arrangements, coherent structures and/or recirculation currents are observed affecting the distribution of the heat transfer coefficients. Measurements of wall temperature as well as of adiabatic wall temperature of the stream are made by means of an infrared scanning radiometer, and the heat transfer coefficients are calculated by means of the so-called heated thin foil technique. The data are reduced in dimensionless form as Nusselt numbers and compared with data from the available literature. Both spatial distributions and averaged values of the Nusselt number are discussed. A new explanation for the second peak in the local Nusselt number is proposed. Keywords: impingement heat transfer, recirculation currents, jet instability, infrared thermography
INTRODUCTION Jets of fluids have been and are still of great interest because of their wide industrial applications. In fact, jets are used to dissipate heat generated by microelectronic circuits, to cool the leading edge of turbine blades, to heat the zones critical for the formation of ice over aircraft, to dry textiles, and to temper glass. Earliest measurements of heat transfer of an air jet impinging on a flat plate were done by Gardon and Cobonpue [1], who considered the influence of nozzle exit diameter, nozzle-to-plate distance, and flow rate (Reynolds number). Later, Gardon and Akfirat [2] accounted for the role of turbulence in heat transfer measurements. Many studies have been made involving jets with and without the same temperature as the ambient fluid, and effects of thermal entrainment have been investigated. In this context, Striegl and Diller [3, 4] developed an analytical model for the case of a single turbulent plane jet. Goldstein et al. [5] carried out experimental studies of recovery factor and local heat transfer for an axisymmetric impinging air jet. Hollworth and Wilson [6] characterized a heated turbulent air jet and performed measurements of mean axial velocity and total temperature in the jet as well as recovery temperature on a fiat surface normal to the jet axis. It is worth noting that heat transfer levels reported by Gardon and Cobonpue [1] and Hollworth and Gero [7] seem to be higher than those shown by Goldstein and
coworkers [5, 8, 9] for short radial distances. Also, Nusselt number values reported in a recent paper by Mohanty and Tawfek [10] are surprisingly higher compared to those in the current literature, in particular the work of Baughn et al. [11, 12]. Discrepancies may be associated with the jet displacement after impingement, which is linked in part to the nozzle shape and in part to the jet-and-plate arrangement. It should be noted that the works reported in the literature include various values of the governing parameters such as the nozzle shape, the outlet diameter, the nozzle length, the position of the nozzle with respect to the plate, and so forth. In addition, some studies are lacking in fundamental information, making generalization of experimental results difficult, As stated recently in the review paper of Viskanta [13], there is considerable discrepancy between the correlations for the average Nusselt number that have been proposed by various workers with respect to the dependence on Reynolds number, spacing ratio, and averaging area. In this context, the way in which Sparrow and Lowell [14] presented results (i.e., recasting data in terms of radial decay) overcomes the drawbacks due to the different test conditions employed by the different investigators and makes a general comparison possible. To our knowledge, the external factors linked to the jet-and-plate arrangement have not been considered adequately. The flat plate is generally considered an open surface; but then, the recirculation currents present in an enclosed surface [15, 16] can still exist when the jet
Address correspondence to Dr. Carosena Meola, Universit~ di Napoli--DETEC, P. le Tecchio, 80, 80125 Naples, Italy.
Experimental Thermaland Fluid Science 1996; 13:29-37 © Elsevier Science Inc., 1996 655 Avenue of the Americas, New York, NY 10010
0894-1777/96/$15.00 PII S0894-1777(96)00011-8
30
Carosena Meola et al.
impinges on a flat plate if there is not sufficient room for the air jet, after impingement, to flow freely toward the ambient. These effects might represent a potential error source leading to contradictory results when the experimental data of different workers are compared. Another aspect to be considered is the occurrence of some jet instabilities observed at certain flow conditions that alter the distribution of the wall temperature with loss of circumferential appearance (for a round nozzle) and the formation of azimuthal structures. Jet instability has been generally analyzed from the point of view of pressure and velocity fluctuations for a self-excited jet [17] or an acoustically forced jet [18]. Recently, Meola et al. [19] recognized the importance of the entrainment effects (which entail fluctuations of pressure and temperature) on the onset of the instability process. Popiel and Trass [20] observed ring-shaped wall eddies using a smoke-wire visualization technique and suggested that these wall eddies could be responsible for the additional enhancement of local momentum and heat or mass transfer and for the second peak in local Nusselt number. Lytle and Webb [21] instead speculated that the outer peak in the Nusselt number was a result of a transition from laminar to turbulent flow in the boundary layer. More details about the disagreement concerning the formation of the outer peak can be found in Viskanta's review [13]. The intention of the present experimental study is to ascertain the presence of the recirculation currents on an open surface when a circular jet impinges on it. The influence of such recirculation currents and of the instability structures on the heat transfer coefficients and particularly on the formation and location of the outer peak is investigated. EXPERIMENTAL SETUP AND TECHNIQUE The experimental apparatus is sketched in Fig. 1. The impingement plate is a thin constantan foil (200 mm wide, 470 mm long, and 0.050 mm thick) held flat by a stiffening fixture. The foil is heated by passing an electric current through it and cooled by an air jet directed perpendicular to it. The electric current is provided with a direct current power supply within 1% uncertainty. The cooling air jet, supplied by a compressor, goes through a pressureregulating valve, a heat exchanger, then, after filtering, to a plenum chamber where pressure and temperature are metered, and then flows through a replaceable nozzle. The nozzle is a truncated cone manufactured with three exit diameters D of 3, 5, and 10 mm, respectively, and
with length L = 50 mm for D = 3 5 mm and L = 100 mm for D = 10 mm. The dimensionless nozzle-to-plate distance Z/D ranges from 2 up to 100, 70, and 30 for the three nozzle diameters. The Mach number M ranges from 0.04 to 0.78 and the Reynolds number Re = V D / v from 10,000 to 173,000; both M and Re are based on the nozzle exit velocity V. In the specific test arrangement (Fig. 1), the nozzle is supported by a flange that is the end of the stagnation chamber. To assess if and how the flange may influence the heat transfer distribution, two stagnation chambers of external diameters 130 and 110 mm are used with supporting nozzle flanges of external diameters 260 and 110 mm, respectively. These chambers are referred to here simply as chamber A and chamber B. A computerized infrared scanning radiometer (IRSR), based on an A G E M A Thermovision 880LW scanner connected via a TIC 8000 A / D converter board to an IBM computer, is employed to measure surface temperatures. The object radiation is detected by means of a mercury cadmium telluride (MCT) element covering the 8-12 /zm band. Nominal sensitivity, expressed in terms of N E T D (noise equivalent temperature difference) is 0.07°C when the scanned object is at ambient temperature. IRSR is applied to the heated thin foil technique, which consists in measuring the convective heat transfer coefficient h between a very thin metallic foil heated by the Joule effect and the air jet impinging on it. The surface temperature distribution is measured by viewing the rear face of the foil, that is, the opposite side of jet impingement. In fact, since the Biot number Bi = hs/kf (where s and kf are the thickness and thermal conductivity of the foil, respectively) is much less than unity (in the present tests Bi ranges from 1.56 × 10 _4 to 5.46 × 10 3), the temperature can be considered practically uniform across the foil thickness. So h is evaluated as
h
Q
Tw- Lw'
where Q is the Joule heating per unit area (corrected for lateral conduction within the foil, radiation, and natural convection losses when not negligible), and Tw and Taw are wall temperature and adiabatic wall temperature of the stream. Each test run consists of two parts. First, with electric current off, the foil surface temperature is assumed to coincide with Taw and the "cold image" is recorded. Second, electric current on, Tw is displayed and the "hot
m~nom~
IIII
I
_thermoeouple
llo, i~mt air supply
[
---e.
nee,die valve
heat exchanger
(~)
camera
traversing system
Figure
1. Experimental setup.
Impingement Heat Transfer 31 image" is recorded. In particular, each image is obtained by averaging 16 images in time sequence. The high sensitivity of IRSR allows keeping Joule heating quite low (450-4800 W / m 2, depending on Re and M values), avoiding high foil temperature. As a result, the electrical resistivity of the foil can be assumed constant. For the employed values of Joule heating, the uncertainty of the absolute temperature measurement is approximately 0.1% of its value. A lens of 7° is used with spatial resolution, at minimum focus distance, of 1 pixel/mm; for better visualization of the formation of instability structures the resolution is increased (to about 3 pixels/mm) by means of an extension ring. The surface of the foil viewed by IRSR is coated with a thin film of black opaque paint with emissivity factor e equal to 0.95. The emissivity factor has been measured, still by the IR system, by relating the detected radiation from a specimen heated by means of a bath/circulator with its actual temperature measured by means of a mercury thermometer. To quantify the influence of the relative position of the jet with respect to the plate, a different arrangement is used, with the plate horizontal and the jet impinging upward. In this case, since it is not possible to maintain the IR scanner with its roll axis in the vertical position (the dewar chamber for the liquid nitrogen cooling the IR detector cannot stand an inclination angle greater than 70°), the image is reflected from a mirror placed at 45 °. To minimize undesired reflection from the surroundings, the entire test apparatus is put in a darkroom while mirror absorption and other eventual radiation losses are taken into account by calibration, by means of a blackbody source, of the thermographic system for the actual test conditions. In the particular application, owing to the necessity of taking experimental readings with high spatial resolution and of detecting the transient circumferential movement of the azimuthal structures, infrared thermography acted as a very effective tool because of its high sensitivity, nonintrusive character, and two-dimensionality [22]. Data presented hereafter do not generally need any correction in the way of image restoration [23]. Furthermore, because of the small temperature differences encountered in the measurement of the adiabatic wall temperature, it is not corrected for radiation and radial conduction. The evaluation of the convective heat transfer coefficient h, instead, needs to take into account both radiation and conduction corrections [24]. So Equation (1) has to be rewritten as
Qh=
-kfs ~
+ ~ O---R- + e~r(T~- TJ) Tw - Taw
(2) where tr is the Stefan-Boltzman constant. Differences between corrected and uncorrected data are generally on the order of 2-6%. H E A T T R A N S F E R MEASUREMENTS Hereafter, heat transfer data, generally averaged over each circumference of given radius R/D, are reduced in
dimensionless form in terms of Nusselt number Nu defined as Nu = hD/k,
(3)
where k is the thermal conductivity of air evaluated at the film temperature and h is calculated from Eq. (2). The Nusselt number is evaluated within an uncertainty of 4-10%.
Influence of the Jet-and-Plate Arrangement Some tests are carried out by employing the experimental arrangement of Fig. 1 (i.e., vertical plate) with chamber A (with a large flange). In such a configuration, a lowpressure zone in the corner where the nozzle is joined to the flange may develop as the jet issues from the nozzle. This, in the case of a short flange-to-plate distance Dp, promotes recirculation currents with flow separation over the plate. At low Reynolds numbers and obviously when the plate is heated, buoyancy effects can originate in the wall jet region (at relatively high R/D values) and can cause a time increase of the jet temperature with consequent time-dependent heat transfer decreasing. This occurrence, in particular, is stressed as the Joule heating is increased. In the present work, buoyancy effects are investigated by means of the schlieren technique and by means of the same IR imaging system by viewing the lateral side of the nozzle. The reversal flow is seen to cross the nozzle or the jet flow (depending on Z/D) at a distance of 30 mm from the plate. Next, a new series of tests are carried out by considering a modified experimental apparatus with the plate positioned horizontally and the jet impinging upward. Different D~ values (35-220 ram) for a fixed Z / D are considered t~at are obtained by lengthening the nozzle with straight ducts of internal diameter equal to the nozzle entrance diameter and of different lengths. The presence of recirculation effects is investigated by following the deflection of a small tuft and by means of the schlieren technique. Two pictures for (a) closed and (b) open impingement surface are shown in Fig. 2. Owing to the difficulty of taking a well-resolved picture from the schlieren image (the streak lines do not have sufficient contrast), two small tufts were glued to opposite sides of the nozzle lip; the flow field can be interpreted from the deflection of such tufts. When a large flange is positioned close to the plate (low Dp values), the jet air, after impingement, is not able to flow freely toward the ambient and comes back to the flange (Fig. 2a). Separation (over the target plate) occurs at about 1.2D from the jet center where, as stated by Martin [25], the vertical component of the jet velocity is decelerated and transformed into a horizontal component. These points of flow separation are generally (also in an open case) present in the jet flow field at short impingement distances and coincide quite well with the location of the well-known vortex rings; in an open case, the flow reattaches downstream at about 2D (depending on the Reynolds number) and follows the surface of the target plate, slightly diverging far away. Separation and reattachment of the jet flow give rise, in terms of heat transfer, to the minimum in the Nusselt number distribution at about 1.2D and to the maximum
32
Carosena Meola et al.
at about 2D; the presence of such minima and maxima in the Nusselt number distribution is widely documented [1, 11-13, 21]. On the other hand, for low Dp values or better, when the flange, as in Fig. 2a, is too close to the target plate, the jet flow, because of the aforementioned low-pressure zone at the nozzle-to-flange junction, is prevented from reattaching and is transformed into recirculation patterns. The essential fact underlying the flow behavior is that the recirculation effects are in contrast to the formation of the outer (second) peak in the local Nusselt number. As Dp is increased, the recirculation tends to vanish and the air jet flows follow the target plate
surface as shown in Fig. 2b. As a consequence, there is local increase in heat transfer, and the lateral peaks in the Nusselt number distribution become more pronounced. At last, the measurements of heat transfer (for the same flow conditions relative to the test arrangements mentioned above) are repeated on an impingement surface made more open by employing the slender chamber B. No recirculation patterns are now observed, and this configuration is assumed to be ideal. The Nusselt number distributions for the different jetand-plate arrangements are shown in Fig. 3 for a truncated cone nozzle of D = 5 mm, Z / D = 2, and Re =
Ca )
(b)
Figure 2. Flow visualization. (a) Closed impingement surface; (b) open impingement surface.
Impingement Heat Transfer 33 50,000. It is evident from the Nusselt number distributions that the test arrangement (with regard to the dimensions of the stagnation chamber), at short impingement distances, drives the flow displacement. In particular, the Nusselt number distribution for the slender chamber B matches quite well the distribution relative to higher D o values for chamber A, indicating that both cases are free of recirculation effects. The Nusselt number distributions for D = 10 mm, Re = 60,000, and several Z / D values, obtained by employing the final ideal experimental setup (horizontal plate and slender stagnation chamber B) without recirculation effects, are shown in Fig. 4. These radial Nu distributions follow the well-known description given by Gardon and Cobonpue [1].
of Flow
Influence
Conditions
•
I
•
"
I
I
I
I
D = 5 ram, Re = 5 0 0 0 0 , Z / D = 2 Chamber B Horiz. plate
Nu
140
,
~
,,,,'•
120
,'
'
.
plat*
'
/-
V e r t ' p l a t e/
220
/
""'.~., - " ' ,
\,
,,
-
,
\-
"35
\
I00
,/
-3
,
-2
,
,
-1
,
i
0
,
~
1
,
J
R/D
\, 3
3. Nusselt number radial distribution for various locations and dimensions of the stagnation chamber.
Figure
Nu
.
,
,
,
,
,
I D= l O m m ' Re = 60000 Z/D
200
150
100
The heat transfer to an impinging jet is governed by flow conditions that are usually summarized by the Reynolds number, the Mach number, and the jet total temperature. The influence of the Reynolds number on the Nusselt number distribution has already been analyzed by previous workers and will not be considered here. As regards the influence of the Mach number, it has been found that when the jet impinges within its potential core at the critical value of the Mach number M = 0.7, the vortex rings break up, giving rise to the formation of azimuthal structures [19]. The presence of such structures can be evidenced through the maps of Taw and Tw reported in Fig. 5, which refers to D = 5 mm, Z / D = 4, and M = 0.78 (Re = 86,400). It is worth noting that data presented in the following text refer, unless otherwise specified, to the final experimental setup (horizontal plate and slender stagnation chamber B), which does not include the undesired effects such as buoyancy and recirculation. As can be seen in Figs 5a and 5b, both t~mperature distributions, Taw and T w, are affected by the jet instability, and the temperature fluctuations are of the same order in both cases. This finding is better shown in Figs. 6 and 7, where the circumferential averages of Taw and Tw are reported for various Mach numbers. Note that
200
250
-2
0
R/D
2
4. Nusselt number radial distributions for various nozzle-to-plate distances. Figure
the distributions of Taw and Tw depend strongly on the Mach number. For M < 0.7 a minimum is present at R / D ~ 1.2; when the Mach number reaches the value of 0.7, this minimum is split into two minima separated by a relative maximum. Since the temperature fluctuations at M > 0.7 for Taw and Tw are of the same order of magnitude, the radial distribution of the Nusselt number, averaged along circumferential patterns, does not show additional peaks as can be seen in Fig. 8. Nevertheless, some azimuthal structures are visible in the two-dimensional map of the Nusselt number (Fig 5c). In addition, the local Nusselt number contours (Fig. 5c) exhibit loss of symmetry about the stagnation point, this effect being due to the transient alternate circumferential movement of the instability structures [19]. By contrast, for low Mach numbers and therefore low Reynolds numbers (e.g., M = 0.3 and Re = 34,000, as shown in Fig. 5d), the flow is not affected by instability, and the Nusselt number contours display circumferential symmetry. Outside the potential core region, the instability starts at a lower Mach number; for instance, at Z / D = 6 the presence of the secondary minima can be noticed already at M = 0.41 because of the mixing, which enters the potential core, entailing entrainment of warmer ambient air. Since the organization of the instability structures is governed by the entrainment of ambient air in the shear layer [19], the test arrangement is of utmost importance. In the case of a close impingement surface, the ambient air is prevented from interfering with the jet while recirculation currents originate at the separation point. As a consequence, the formation of the instability structures is contrasted. The data considered so far refer to the total jet temperature TO close to the ambient temperature Ta. The temperature difference between TO and Ta drives the entrainment and affects the Nusselt number distribution. In this way, from preceding arguments in this paper, it is clear that the dependency on the temperature difference has to be considered within the specific test arrangement. In particular, a hot air jet impinging on a vertical plate displays upward movement of the stagnation point, split-
34
Carosena Meola et al. ,
i
,
|
1
4 Y/D
Y/E
2
2
0
-2
-2
\
/
-4
_4 ¸
"z¢~-~ I
-4
I
-2
I
0
I
I
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2 X/D 4
-4
a)
!
I
I
-2
0
2
I
0
2 X/D 4
XID4
b) %
4
4
Y/D 2
0
0
-2
-2
-4
-4 I
-4
-2
0
2 X/D 4
c)
-4
-2
d)
Figure 5. Two-dimensional maps. (a) Taw (K); (b) Tw (K); (c) Nu for D = 5 mm, Z / D = 4, and M = 0.78; (d) Nu for D = 5 ram, Z / D = 4, and M = 0.3.
ting it into two contiguous stagnation points. This effect is not evident when the jet impinges upward on a horizontal plate, in which case rotation of the w a r m e r jet air surr o u n d e d by the cold ambient air is observed. Obviously, the flow dynamics d e p e n d on the impingement surface configuration, open or closed. M o r e a p p r o p r i a t e investigations into the flow behavior with variation of the thermal boundary conditions are still under way. However, it is well known that the potential core tends to shorten as the jet t e m p e r a t u r e increases. As shown in Fig. 9, which refers to impingement on a horizontal plate, the outer Nu peaks relative to Z / D = 4 for To - Ta = 4 0 ° C b e c o m e much milder and Nu values around the stagnation point increase, to approach the distribution relative to Z / D = 6 for T0 - Ta = 0 ° C .
DISCUSSIONS AND DATA CORRELATIONS In light of the available literature and the present results, there is some evidence to support the hypothesis [20] that the vortex rings could be responsible for the formation of the second p e a k in the local Nusselt number. The vortex rings, for M < 0.7 [19], keep their structure after impingment, as the annular minima present in the temperature distribution of Figs. 6 and 7 show. A vortex ring acts as an obstacle in the free stream and causes separation and turbulent reattachment downstream. The reattachment point coincides with the maximum in heat transfer, and its location depends on the magnitude of the vortex rings. As the Mach number increases (the vortex ring stretches), the p e a k moves downstream, as was also observed by Lytle
Impingement Heat Transfer 400
!
300
D=5mm, Z/D=4
35
/
D = 5 mm, Z/D =4 =0.78
Taw
M=0.41
O) " ' - , ",
0"7!0.67 "'~'
0.56.67
300 .56
295
•
00.75/ "71/'/
290 -,
\ ~ - ' / i~f
I
I
I
-2
0
2
100 R/D
!
I
I
......."
. • = 0 . 4 1. / / ; 4
300
;~--/--.,
,,,
0
2
R/D
4
mal boundary conditions. It must be remarked that the recirculation currents oppose the flow reattachment and the formation of the outer peak (Fig. 3). Finally, the effects of the jet instability and the recirculation currents on the average Nusselt number are investigated. Data are averaged over a circular area of radius 6 times the nozzle diameter. First, only data relative to an ideal experimental apparatus without the two phenomena mentioned above are considered. Following the empirical correlations proposed by Klammer and Schupe and reviewed by Viskanta [13], it is found that the Nusselt number depends on the Reynolds number to the 0.65 power, and this is in general agreement with Martin [25]. Values of N u / R e °65 are plotted against Z / D in Fig. 10 for the three nozzle diameters, R / D = 6, and 10,000 < Re < 100,000. As can be seen, the average Nusselt number is independent of Z / D for Z/D < 10, while the correlation curve for Z/D > 10 is Nu = 0.548
Re°65(Z/D)-0714.
D=lOmm, Re=
(4)
To - Ta = 40 *C Z/D=4
To=Ta
Nu
........
/,.~
Z/D=4
../~
.........................
-2
Figure 8. Influence of Mach number on Nu radial distribution.
200
Tw;
0.56
-,
4
and Webb [21]. At a Mach number of 0.7 the vortex rings break up upon impact with the wall, leading to entrainment of warmer ambient air. As a consequence, two minima with a maximum between them are formed (Figs. 6 and 7) that are associated with the splitting of the primary vortex ring into two secondary vortex rings. The peak in the Nusselt number, as shown in Fig. 8, moves upstream, following the location of the first vortex ring, which is now closer to the jet center. It is worth noting that the distributions shown in Fig. 8 are obtained by averaging data over circumferences of given radius; conversely, after breakup, azimuthal structures are formed (Fig. 5c) and the outer peak assumes different values from point to point over the same circumference. The radial position of the outer peak moves toward the jet center as the impingement distance is reduced [21], and that is linked to the variation of the location of the primary vortex ring with the impingement distance [19]. On the other hand, the jet displacement after impingement is governed by the test arrangement as well as by the ther-
D = 5 mm, Z/D = 4
04
21)0
~tt ~~'-¢1 ~,..~,,
Figure 6. Tdw radial distributions for various Mach numbers.
305
""
"
150
/.'...,.-7 100
0.78/~/ 295
0.75 0.71
-4
I
I
I
-2
0
2
50 R/D
4
Figure 7. Tw radial distributions for various Mach numbers.
-6
!
I
I
I
I
-4
-2
0
2
4
R/D
Figure 9. Influence of the jet total temperature.
6
36
Carosena Meola et al.
a
10 -t
Nu Re065
°: iiiiiiiii t ,Re o
10 mm (Re = 1 0 0 0 0 - 1 0 0 0 0 0 )
A
1 0 -2
I
I
I0
Z/D
100
Figure 10. Correlation for the average Nu number.
In addition to jet instability effects, it has already been observed that the Nusselt number is affected only locally (Fig. 5c) by the azimuthal structures. The spatial distributions obtained by averaging the Nu values along circumferential patterns are quantitatively analogous to the ones for the ideal case (Fig. 8), and similar behavior is, of course, found for the average values over a circular area. The recirculation currents instead have strong effects on the average Nusselt values and can cause a decrease of 20% at the shorter impingement distances. The recirculation currents, in fact, favor the flow separation and contrast the reattachment. As a consequence, the lateral peaks are destroyed with a smooth decrease in the Nusselt number distribution, which now takes the form of a bell shape. A comparison of the three correlation curves relative to the three cases--ideal, with instability, and with recirculation--is shown in Fig. 11. PRACTICAL SIGNIFICANCE/USEFULNESS Fluid jets are of great interest because of their wide industrial applications. In fact, jets are used to dissipate
10 -~
O
0
I-I
Nu
Re0.65
ideal
O recirculation
D instability
10"2
z~
I 10
Z/D
Figure 11. Influence of instability and recirculation currents on the average Nusselt number.
heat generated by microelectronic circuits, to cool the leading edge of turbine blades, to heat the zones critical to the formation of ice over aircraft, to dry textiles, and to temper glass. The external factors linked to the jet-andplate arrangement have not been considered adequately before. The fiat plate is generally considered an open surface; but then, the recirculation currents present in an enclosed surface can still exist when the jet impinges on a fiat plate if there is not sufficient room for the air jet, after impingement, to flow freely toward the ambient. The present experimental study on impingement heat transfer focuses attention on some phenomena induced in the shear layer by flow conditions and impingement setup. From a practical standpoint, the phenomena of recirculation currents and azimuthal structures arising in the local flow field are of great importance in obtaining results that can be used for different applications. Both of the effects mentioned above may result in undesired temperature distributions over the surface under treatment and can pose a serious problem in practical applications where precise standards are required. In particular, the recirculation currents induce a decrease of about 20% (at short impingement distances) in the average Nusselt number with respect to the ideal case.
CONCLUSIONS An experimental investigation into convective heat transfer coefficients between a flat plate and a round air jet impinging on it has been made in an attempt to assess the dependency of the second peak in the Nusselt number on shear layer dynamics. The critical difference in opinion [20, 21] as to how the outer peak is achieved, evidenced by Viskanta in his review [13], has been analyzed accurately. As the major conclusion of the present work (on account of the high spatial resolution of infrared thermography), there is experimental evidence to argue that the vortex rings are responsible for the second Nu peak as was speculated by Popiel and Trass [20]. The formation and location of the outer peak may be considered a result of flow reattachment rather than a simple transition from laminar to turbulent. It has to be pointed out as a matter of particular importance that the jet-and-plate arrangement plays a key role in the flow displacement after impingement. Recirculation currents can exist also on a flat plate if there is not sufficient free room for the air jet to flow downstream and can interfere with the formation of the outer peak. From a practical standpoint, the phenomena (recirculation currents and azimuthal structures) arising in the local flow field are of great importance in obtaining results that can be used for different applications. Both of the effects mentioned above may result in undesired temperature distributions over the surface under treatment and might be a serious problem in practical applications where precise standards are required. The instability structures show only local effects; minima and maxima compensate each other when averaging data over circular areas. The strong effects of the recirculation currents instead remain after that average is obtained. In particular, the recirculation currents induce a decrease of about 20% (at short impingement distances) in the average Nusselt number with respect to the ideal case.
Impingement H e a t Transfer
NOMENCLATURE Bi D Dp h
Blot n u m b e r ( = h s / k O , d i m e n s i o n l e s s nozzle exit d i a m e t e r , m c h a m b e r f l a n g e - t o - p l a t e distance, m c o n v e c t i v e h e a t transfer coefficient [see Eq. (2) for definition], W / ( m 2- K) k t h e r m a l conductivity o f the air, W / ( m • K) kf t h e r m a l conductivity o f the foil, W / ( m • K) L n o z z l e length, m M Mach number, dimensionless N u local Nusselt n u m b e r ( = h D / k ) , d i m e n s i o n l e s s N u a v e r a g e Nusselt n u m b e r ( = h D / k ) , d i m e n s i o n l e s s Q J o u l e heating, W R radial distance f r o m j e t center, m R e jet R e y n o l d s n u m b e r ( = V D / v ) , d i m e n s i o n l e s s s foil thickness, m Za a m b i e n t t e m p e r a t u r e , K Taw adiabatic wall t e m p e r a t u r e , K Tw wall t e m p e r a t u r e , K V velocity at nozzle exit, m / s X, Y Z
spatial c o o r d i n a t e s (~/X 2 + y Z = R), m i m p i n g e m e n t distance, m G r e e k Symbols emissivity coefficient, d i m e n s i o n l e s s k i n e m a t i c viscosity o f the air, m 2 / s
Subscript 0
stagnation conditions REFERENCES
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37
8. Goldstein, R. J., and Franchett, M. E., Heat Transfer from a Flat Surface to an Oblique Impinging Jet, Trans. ASME 110, 84-90, 1988. 9. Goldstein, R. J., Sobolik, K. A., and Seol, W. S., Effect of Entrainment on the Heat Transfer to a Heated Circular Air Jet Impinging on a Flat Surface, Trans. ASME 112, 608-611, 1990. 10. Mohanty, A. K., and Tawfek, A. A., Heat Transfer Due to a Round Jet Impinging Normal to a Flat Surface, Int. J. Heat Mass Transfer 36, 1639-1647, 1993. 11. Baughn, J. W., and Shimizu, S., Heat Transfer Measurements from a Surface with Uniform Heat Flux and an Impinging Jet, Trans. ASME J. Heat Transfer 111, 1096-1098, 1989. 12. Baughn, J. W., Hechanova, A. E., and Yan, X., An Experimental Study of Entrainment Effects on the Heat Transfer from a Flat Surface to a Heated Circular Impinging Jet, Trans. ASME J. Heat Transfer 113, 1023-1025, 1991. 13. Viskanta, R., Heat Transfer to Impinging Isothermal Gas and Flames Jets, Exp. Thermal Fluid Sci. 6, 111-134, 1993. 14. Sparrow, E. M., and Lovell, B. J., Heat Transfer Characteristics of an Obliquely Impinging Circular Jet, Trans. ASME J. Heat Transfer 102, 202-209, 1980. 15. Jusionis, V. J., Heat Transfer from Impinging Gas Jets on an Enclosed Concave Surface, Eng. Notes 7, 87-88, 1970. 16. Meo!a, C., no, G. M., Riegel, E., and Salvato, F., An Experimental Study of an Anti-Icing Hot Air Spray Tube System, 19th Cong. Int. Council Aeronaut. Sci., 3, 2345-2351, Anaheim, CA, 1994. 17. Donaldson, C. D., and Snedeker, R. S., A Study of Free Jet Impingement. Part I. Mean Properties of Free and Impinging Jets, J. Fluid Mech. 45, 281-319, 1971. 18. Didden, N., and Ho., C. M., Unsteady Separation in a Boundary Layer Produced by an Impinging Jet, J. Fluid Mech. 160, 235-256, 1985. 19. Meola, C., de Luca, L., and Carlomagno, G. M., Azimuthal Instability in an Impinging Jet: Adiabatic Wall Temperature Distribution, Exp. Fluids 18, 303-310, 1995. 20. Popiel, C. O., and Trass, O., Visualization of a Free and Impinging Round Jet, Exp. Thermal Fluid Sci. 253-264, 1991. 21. Lytle, D., and Webb. B. W., Secondary Heat Transfer Maxima for Air Jet Impingement at Low Nozzle-to-Plate Spacing, in Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics, J. F. Keffer, R. K. Shah, and E. N. Ganic, Eds., pp. 776-783, Elsevier, New York, 1991. 22. Carlomagno, G. M., and de Luca, L., Infrared Thermography in Heat Transfer, in Handbook of Flow Visualization, W. J. Yang, Ed., pp. 531-553, Hemisphere, New York, 1989. 23. de Luca, L., Computerized IR Thermography for Convective Heat Transfer Measurements, in Computational Methods and Experimental Measurement, A. Sousa, C. A. Brebbia, and G. M. Carlomagno, Eds., pp. 347-358, CMP/Elsevier, New York, 1991. 24. de Luca, L., Cardone, G., and Carlomagno, G. M., Fluid Dynamics Applications of IR Imaging System, in Quantitative Infrared Thermography QIRT 92, D. Balageas, G. Busse, and G. M. Carlomagno, Eds., Editions Europeennes Thermique et Industrie, Paris, pp. 98-104, 1992. 25. Martin, H., Heat and Mass Transfer Between Impinging Gas Jets and Solid Surfaces, Adv. Heat Transfer 13, 1-60, 1977.
Received October 10, 1995; revised February 7, 1996