OPTICAL INVESTIGATIONS OF NATURAL CONVECTION IN VERTICAL CHANNELS

Transcription

1 7TH INT SYMP ON FLUID CONTROL, MEASUREMENT AND VISUALIZATION OPTICAL INVESTIGATIONS OF NATURAL CONVECTION IN VERTICAL CHANNELS D. Ambrosini*, D. Paoletti*, G. Tanda**, G. Galli*** *INFM - Dip. Energetica Università dell Aquila, **DITEC Università di Genova ***Dip. Fisica Tecnica Università di Roma La Sapienza Keords: optical techniques, heat transfer, aerodnamics, schlieren, holograph ABSTRACT Heat transfer phenomena, hich frequentl involve convection, are usuall described through a convective heat transfer coefficient h. To obtain a precise measurement of h can be difficult, since calculation requires knoledge of the temperature gradient beteen the solid surface and the fluid, measured, possibl, ithout disturbing the thermal laer. Optical techniques are poerful tools in experimental analsis because of their non disturbing nature. In this ork the natural convection heat transfer in vertical channels is investigated b appling to different optical techniques, namel schlieren and holographic interferometr. Experiments ere conducted at DITEC, Universit of Genova (Ital) and at the Energetic Dept. of the Universit of L Aquila (Ital) on the same test sections. 1 INTRODUCTION Heat transfer phenomena frequentl involve thermal convection, e.g. energ transfer beteen a solid all and a fluid as a result of both conductive heat transfer and fluid motion. Convection is usuall described through a heat transfer coefficient, h, hich is a function of the all-to-fluid temperature difference, the fluid temperature gradient at the all, and the fluid thermal conductivit. It is generall recognized that optical techniques are poerful tools to investigate heat transfer in transparent fluids because the enable the simultaneous, real-time analsis of large fluid regions to be performed in the absence of instrument probes hich could influence the phenomenon [1-3]. Optical techniques based on interference rel on differences in lengths of the optical paths, hereas shadograph and schlieren techniques utilize the deflection of light in the measurement media. Although all these techniques depend on variation of the index of refraction in a transparent fluid and the resulting effects on a light beam passing through the test region, different quantities are measured ith each one. Therefore, each technique involves the use of specific instrumentation, ith experimental uncertainties and ranges of applicabilit, hich differ from case to case. In this ork, a comparison is made beteen to different optical methods in investigating a tpical problem of natural convection: heat transfer in vertical channels. Free convection in channels is encountered in a number of technological applications: most of the existing data are correlated in [4]. The channel, consisting of to parallel vertical plates at a given spacing value, as asmmetricall heated at uniform all temperature. Local heat transfer coefficients and isotherm patterns ere recovered b using the schlieren technique [5] and the holographic interferometr technique [6]. Experiments ere conducted at DITEC, Universit of Genova and at the Energetic Dept., Universit of L Aquila on the same test sections. 1

2 D. Ambrosini, D. Paoletti, G. Tanda, G. Galli Fig. 1 - Schematic vie (left) and photograph (right) of the test section ith smooth channels 2 THE EXPERIMENTS 2.1 Test section The test section is shon in Fig. 1. It consisted of a plate (termed "heated plate"), made up of to aluminum sheets ith three plane electrical resistances sandiched in beteen, and to shrouding vertical alls. The plate, verticall suspended, is heated b suppling a given amount of poer to the resistances. The shrouding alls ere smooth, unheated and placed so as to form to adjacent, smmetrical, vertical channels. Aluminum as chosen for its high thermal conductivit, lo thermal emittance, and eas machinabilit. The dimensions of the heated plate ere the folloing: overall thickness t = m, height H = m, length L = 0.3 m. The length as set much greater than the other dimensions in order to favour a to-dimensional thermal field in the channels. The unheated shrouding alls, having the same height and length as the heated plate, ere made up of 3 mm-thick sheets of Perspex, covered ith a reflective plastic film on the sides facing the aluminum plate (to reduce radiant exchange) and insulated b a 0.02 m laer of polstrene on the outer surfaces (to minimize heat conduction through the side alls). The spacing S beteen each unheated all and the heated plate, set equal on both sides, as varied in order to ield a channel aspect ratio S/H equal to 0.3. Both the plate and the surroundings ere instrumented ith fine-gauge, chromelalumel thermocouples, calibrated to ± 0.1 K. Numerous thermocouples ere embedded in the all of the heated plate at different locations through 0.5 mm-dia holes drilled into the rear surfaces of the to coupled aluminum sheets. Care as taken to drill the holes as close to the exposed surfaces as possible. The ambient air temperature as measured b five shielded thermocouples situated just belo the plate arra. Additional thermocouples ere used to detect surface temperature on the unheated side alls. The plate can be considered isothermal. In fact for all experimental runs, the temperature readings ere uniform ithin ± 2% of the mean plate-to-ambient temperature difference. The radiation heat transfer as expected to be small because of the lo thermal emittance of aluminum surfaces, hich as measured b a radiometric apparatus as 0.12 ± in the temperature range of interest. The distance of the leading edge of the plate from the floor surface as about 1.4 m for schlieren experiments, hile it as reduced to onl 0.2 m for holographic interferometr 2

3 OPTICAL INVESTIGATIONS OF CONVECTION IN CHANNELS experiments, due to the requirement of placing the test section on an optical table. A separate set of experiments shoed that the shorter distance adopted in interferometric runs did not significantl affect the thermal field inside the channels. Fig. 2 - Schematic laout of the Schlieren apparatus Supplementar experiments ere also carried out in the presence of transverse, squarecross-sectioned, aluminum ribs periodicall placed on the heated plate. Five square ribs (4.85 mm high) for each side of the heated plate ere considered. 2.2 The Schlieren technique A schlieren optical sstem as used to reconstruct the thermal field and to perform measurements of local heat transfer coefficients. The schlieren sstem is schematicall shon in Fig. 2. A noncoherent light beam from a vertical slit source, collimated b the concave mirror M 1, passes through the test section. A second concave mirror M 2, is then used to project a real image of the slit source in the focal plane and a real image of the test section onto a screen or camera. Oing to the inhomogeneities of the fluid refractive index around the heated plate, the light ras undergo angular deflections. Regions of the optical field characterized b the same light deflection in the -z plane can be identified b shifting an opaque vertical filament in the focal plane of mirror M 2. When a disturbed light ra is stopped b the focal filament, the image of the corresponding region of fluid ill appear dark on the screen, hile the remaining field ill be bright. The deflection α of a disturbed ra can be recorded b measuring, in the focal plane of mirror M 2, the distance beteen the middle of the undisturbed image of the slit source and the centerline of the filament. It can be easil shon that the distance (corresponding to the ra shift at the focal plane of mirror M 2 ) is given b f 2 α, f 2 being the focal length of the mirror M 2. If the thermal field is assumed to be to-dimensional (i.e. temperature is independent of the 3

4 D. Ambrosini, D. Paoletti, G. Tanda, G. Galli z-coordinate) the shift of each light ra can be related to the local temperature gradient in the fluid b the folloing expression Ω T = (1) 2 T here T = T(x, ) is the fluid (absolute) temperature, is the direction in hich the light deflection is recorded and Ω is a constant depending on the fluid, the pressure, the length of the heated plate and the geometric parameters of the optical components. In the present experiment, Ω as equal to m 2 K. The temperature reconstruction procedure is based on a set of photographs (for each experimental run) obtained ith the focal filament placed at different distances from the undisturbed slit-source image. B identifing, for each photograph, the coordinates of the centerline of the filament shado, it is possible to obtain the profile of lines of constant light-deviation values and thus, taking into account Eq. (1), to reconstruct the temperature distribution in the entire optical field. The local heat transfer coefficient can be directl obtained from schlieren images ithout reconstructing the hole thermal field. Indeed, if the focal filament is moved until its shado intersects the vertical surface profile in the image projected on the camera, the displacement of the filament corresponds to the deviation of the light ra passing in the vicinit of the all at the desired location. The relation beteen light deviation and the local heat transfer coefficient can be easil shon as follos. B appling Eq. (1) to the heated alls, one obtains Ω T = (2) 2 T here ( T / ) is the fluid temperature gradient, in the direction normal to the plate surface, evaluated at the all, and T is the all temperature. B introducing the local heat transfer coefficient, defined as h = k T ( T T ) (3) here k is the thermal conductivit of the fluid at the all temperature and T is the ambient (or inlet) air temperature, it follos that k T h = Ω ( T T 2 ) (4) The uncertaint (at the 95% confidence level) in local heat transfer coefficient h as estimated to range from 8 to 12 %, hile the uncertaint in the reconstructed temperature T as about 2-4 % of the all-to-ambient temperature difference (i.e K for the present experiment). Further details on the derivation of fundamental schlieren formulae as ell as of the thermal field reconstruction procedure are given in [7, 8]. 4

5 OPTICAL INVESTIGATIONS OF CONVECTION IN CHANNELS Alternativel, a series of schlieren images can be obtained b using the colour-image sstem, in hich a coloured filter (thin transparent coloured strips) is placed in the focal plane of mirror M 2, in lieu of the focal filament. The strips must be used ith a slit source, hich must be in vertical position if horizontal temperature gradients are to be detected. Temperature inhomogeneities in the test section cause the deflected ras to pass through different coloured strips of the filter. Therefore, the image of all the points, hich deflect the light beam through the same angle, has the same colour. Colour schlieren method enables a hole-field visualization of the phenomenon, ithout the need of moving the filter and of superimposing different images. Unfortunatel, the measurement range is limited and therefore colour schlieren can be used onl for qualitative visualization. Fig. 3 - Schematic laout of the holographic interferometr apparatus 2.3 The holographic Interferometr technique The experimental laout, shon in Fig. 3, is the usual one for holograms recording [1, 6]. An Argon-ion laser beam (ith avelength λ = nm and a poer of 500 mw) is divided b a beam splitter into object and reference beams. The object beam is expanded b a microscope objective, filtered b a pinhole and finall collimated to 160 mm diameter. The resulting parallel ras cross the test section. Double-exposure holographic interferometr involves the registration of to holograms on the same photographic plate. The first hologram is recorded ith the test section at ambient temperature. After heating the plate at the fixed temperature, the second hologram is recorded. The photographic plate is developed and fixed and then it is exactl repositioned and illuminated b the reference beam. A re-illuminated hologram reconstructs the object both in amplitude and phase. In double-exposure holograph, the object is independentl reconstructed in its to states. The to reconstructing aves interfere, thus producing an interference pattern onto the three-dimensional virtual image of the object. These fringes identif regions shoing the same phase variation. Let us consider a light beam that crosses the test region (length L along the propagation axis). The phase variation experienced b the beam ϕ is related to the refractive index variation ( n n ) through the folloing equation 5

6 D. Ambrosini, D. Paoletti, G. Tanda, G. Galli 2π ( n n ) L = ϕ (5) λ valid for a to-dimensional flo. On the other hand, for gases the relation beteen index of refraction and temperature can be described b the Gladstone-Dale equation C n = 1 + (6) T In the present experiment C = K. From Eqs. (5) and (6) it can be seen that fringes (isophase lines) are also isothermal lines and therefore the image is a sort of topographic map of the temperature field. Taking into account that the phase difference beteen to adjacent fringes is 2 π and inserting Eq. (6) into Eq. (5), one obtains for each fringe a constant temperature value as follos T 1 = + λ + 1 i Ti LC 1 (7) Fringes are counted b assigning number N = 0 to the large bright fringe in the undisturbed ambient. Subsequent bright fringes are assigned numbers N = 1, 2, 3 hile the centers of all dark fringes are assigned numbers N = 0.5, 1.5, 2.5 Temperatures of undisturbed air (N = 0) and of the hot plate (maximum N) are knon. The temperature distribution can be obtained b simpl measuring the distance beteen successive fringes on the interferogram. The fluid temperature gradient is calculated b performing a least squares fitting of the temperature data. Then, the local heat transfer coefficient can be evaluated through Eq. (3). The uncertaint (at the 95% confidence level) in local heat transfer coefficient h as estimated to range from 5 to 10%, hile the uncertaint in the reconstructed temperature T as about K. This uncertaint is independent of the all-to-ambient temperature difference. The performance of this technique could be improved b using different experimental setups (e.g. sandich holograph) and/or data processing [9, 10]. 3 RESULTS AND DISCUSSION Experimental runs ere conducted b imposing a mean temperature difference beteen the heated plate and the ambient air of 45 K (schlieren experiment) and 28 K and 20 K (holographic interferometr experiment). A first set of experiments as conducted b the colour schlieren method on both the smooth and the ribbed channel. Fig. 4 as obtained ith the colour filter mounted verticall, in order to visualise regions of fluid in the channel ith non-negligible horizontal temperature gradients. Images ere recorded under stead state conditions and for an aspect ratio, namel S/H equal to 0.3. As it is apparent from the images, the colour pattern is smmetrical and the flo is laminar (no disturbances in the colour contours). A large part of the fluid in the channel appears light blue, hich is the colour associated ith negligible thermal gradients. The adiabatic plate does not seem to affect the thermal field and the phenomenon resembles the heat transfer from a single, vertical heated plate. Stronger gradients are present near the plate (ello, green, red and blue) and along the vertical sides of the ribs, hen present. Colour schlieren images recorded ith the colour filter mounted horizontall sho that non-zero vertical temperature gradients 6

7 OPTICAL INVESTIGATIONS OF CONVECTION IN CHANNELS occur onl in the vicinit of the leading and trailing edges of the heated plate and close to the horizontal sides of ribs, hen present. Then the test section as investigated to obtain (b the focal filament method) lines of constant light-deviation and, according to the procedure outlined in section 2.2, the convective heat transfer. The contours of lines deflecting the light b the same amount are given in Fig. 5. Because of the smmetric configuration of the test section, results are reported onl for one of the to identical adjacent channels. Fig. 4 - Colour schlieren images (S/H = 0.3) for the smooth (left) and the ribbed channel (right) Fig. 6 shos double-exposure holograms, recorded ith S/H = 0.3 and a temperature difference of 28 K, for the smooth channel (left) and 20 K for the ribbed channel (right). Schlieren and holographic experimental runs ere performed at different plate-to-ambient temperature differences. As a matter of fact, the search for best conditions for each of the to techniques, hich have different sensitivit, can preclude the stud of the same temperature difference. The use of a temperature difference of 45 K gives a ver dense fringe pattern in holographic interferometr, hich is difficult to analze quantitativel. On the other hand, a 28 K (or 20 K) difference can be difficult to analze ith schlieren. Taking into account that black fringes are isothermal lines, a qualitative investigation of the fringe patterns confirms the smmetrical and laminar nature of the phenomenon and the influence of non-zero vertical temperature gradients onl in the vicinit of the loer edges of the aluminum plate. Further insight into the techniques performance can be obtained b examining the variation of the local Nusselt number along the vertical plate. The Raleigh numbers Ra H ere 1.8x10 7 (schlieren experiments), 1.3x10 7 and 9.7x10 6 (holographic experiments). Experimental results, in terms of local Nusselt number, can be compared ith Ostrach s correlation for a single, vertical heated plate, Nu x = Ra x This comparison, depicted in Fig. 7 is of particular interest. As it is evident from inspection of the figures, the results presented are in ver good agreement ith each other. Moreover, the agreement ith Ostrach s correlation is ver good for the aspect ratio S/H = 0.3. This as expected; in fact for this value of the aspect ratio, the influence of the adiabatic adjacent all is negligible. 7

8 D. Ambrosini, D. Paoletti, G. Tanda, G. Galli Fig. 5 Lines of constant light deviations obtained b Schlieren images (S/H = 0.3) for the smooth (left) and the ribbed channel (right) Fig. 6 Double-exposure holograms shoing the isotherms in the channels: S/H = 0.3 and temperature difference of 28 K (left, smooth channel) and 20 K (right, ribbed channel). 8

9 OPTICAL INVESTIGATIONS OF CONVECTION IN CHANNELS Fig. 7 Local Nusselt number vs. local Raleigh number for the smooth channel (S/H = 0.3) 4 CONCLUSION Natural convection heat transfer as experimentall investigated for smooth and ribbed vertical channels. To different optical techniques, namel holographic interferometr and schlieren, ere used to visualize the temperature gradient field or the temperature field and to obtain local Nusselt numbers. The experiments reported here indicate that each technique has its on features, but their combination proves ver useful in reducing inherent shortcomings, hile providing a greater amount of quantitative and qualitative data. Further experimental investigations, especiall for ribbed channels, are under progress. REFERENCES 1. Hauf W., and Grigull U. Optical methods in heat transfer in J.P. Hartnett, T.F. Irvine Jr. (eds.), Advances in Heat Transfer, vol. 6. Academic Press, Ne York, Mainger F. (ed.). Optical Measurement. Springer-Verlag, Berlin, The ebsite of Optical Methods in Heat and Mass Transfer (OMHAT): 4. Bar-Cohen A., and Rohseno W. M. Thermall optimum spacing of vertical, natural convection cooled, parallel plates. ASME J. Heat Transfer, vol. 106, pp , Settles G. S. Schlieren and Shadograph techniques. Springer, Berlin, Vest C M. Holographic Interferometr. Wile, Ne York,

10 D. Ambrosini, D. Paoletti, G. Tanda, G. Galli 7. Tanda G. Natural Convection Heat Transfer From a Staggered Vertical Plate Arra. ASME J. Heat Transfer, vol. 115, pp , Devia F., Milano G., Tanda G. Evaluation of Thermal Field in Buoanc-Induced Flos b a Schlieren Method. Experimental Thermal and Fluid Science, vol. 8, pp.1-9, Ambrosini D., Paoletti D., Schirripa Spagnolo G. Sandich holograph for simultaneous temperature visualization and heat-transfer coefficient measurement. Opt. Eng., vol. 40, pp , Schirripa Spagnolo G., Ambrosini D., Ponticiello A., Paoletti D. Temperature measurement in laminar free convection using electro-optic holograph. J. Phs. III France, vol. 7, pp ,