FLOW AND HEAT TRANSFER AROUND THE FLAT PLATE INSTALLED IN A RECTANGULAR DUCT WITH FLOW PULSATION

ISTP-16, 2005, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA FLOW AND HEAT TRANSFER AROUND THE FLAT PLATE INSTALLED IN A RECTANGULAR DUCT WITH FLOW PULSATION Hironori SAITOH* *Dept. of Mechanical Engineering, SOJO University Ikeda 4-22-1, Kumamoto, 860-0082 Japan Tel:(+81)-96-326-3729, Fax:(+81)-96-323-1351, E-mail: saitoh@mec.sojo-u.ac.jp Keywords: Heat Transfer, Flow Pulsation, Velocity Fluctuation, Flow Visualization, Vortices Abstract This study deals with flow behavior and associated heat transfer in pulsating duct flow. The effect of pulsating frequency on flow and heat transfer characteristics around the flat plate installed in a rectangular duct was experimentally investigated. Mechanism of heat transfer enhancement or prevention with flow pulsation is discussed in this paper based on the visualization results of flow and temperature fields. 1. Introduction Present high performance of thermal devices and equipments has been achieved by the fundamental studies of convection heat transfer. Such devices, at present, are almost already matured. Breakthrough technologies are required for further improvements of their performance. Flow behavior is the most important interest for convection cooling/heating applied various kinds of thermal devices, heat engines, power plants, process engineering and so on. Almost all of such applications, however, have poor controllability of flow field because they are basically designed for their operation with steady flow. Flow pattern is dominated by only flow rate and geometrical shape of the passage. Considering higher controllability of flow field, I focused on heat transfer in pulsating flow. Unsteady flow with pulsation has several parameters such as mean flow rate, frequency and amplitude which govern flow behavior. Pulsating flow and heat transfer have been studied extensively and reported by a number of researchers [1-18] for laminar, turbulent regions and transition from laminar to turbulent. In spite of more than thirty-year history of these studies, flow structure with periodical velocity fluctuation and its effect on heat transfer are still at question. Some researchers showed conflicting results. Niida et al. [1]; Bayley et al. [2]; Fujita and Tsubouchi [3] reported heat transfer enhancements due to flow pulsation. On the contrary Miller [4] and Jackson and Purdy [5] concluded no impact of flow pulsation on heat transfer. Although their experimental conditions were different from each other, many of them focused on the relationship between heat transfer and periodic or bulk flow reversal. Kearney et al. [6] pointed out the reason of these conflicting results that the physics of the unsteady convection process over an exceptionally broad parameter space are not fully understood. Kearney et al. [6] emphasized on the necessity of time-resolved boundarylayer temperature data for correct understanding of heat transfer characteristics in pulsating flow and they employed CARS (Coherent Anti- Stokes Raman Scattering) technique. Fujita and Tsubouchi [3] also obtained time-resolved heat transfer data on a flat plate by Schlieren interaction method. Above introduced two studies showed the time-resolved data of temperature field, however, data of flow field was depended on local point measurements by hot wire anemometer. In order to clear the complicated unsteady flow structure with 1

Hironori Saitoh periodical velocity fluctuation and its effect on heat transfer, macroscopic observation of both the flow and temperature fields must be needed. The objective of this study, therefore, is to make clear the pulsating flow structure and heat transfer characteristics based on the visualizations of flow and temperature fields. 2. Heat Transfer Experiments 2.1 Experimental Setup and Methods Figure 1 shows a schematic of the test section. The test section consists of a duct, 446 mm in length with 100 mm 100 mm square cross section and a flat plate. The duct has one pair of windows for Schlieren visualization. The flat plate simulates a bulkhead of the tube bundle of a heat exchanger a plate fin and so on. This is constructed from two Bakelite pieces and installed in the mid-plane of the duct cross section as shown in fig.1 (A-A cross section). Two films of stainless heater, 0.02 mm in thickness, were attached on the both sides of the flat plate. One was used as main heater as the heat transfer surface and the other was set as guard heater to realize negligible small heat loss across the plate. K-type (Chromel-Alumel) thermocouples, 0.2 mm in diameter, were attached on the back side of the main heater and their wire bundle was taken out of the test section through the space inside the flat plate. In the experiments seven-point temperature measurement in flow direction was conducted under constant heat flux condition. Figure 2 represents a general view of the entire experimental setup. Operating fluid (air) was supplied through pulsation generator into the test section and exhausted to atmosphere through a surge tank by means of a Sirroco fan. Mean flow rate was measured by hot-wire anemometer in the exhaust pipe connected with the surge tank. Pulsation generator consists of a valve and an eccentric cam connected with pully and motor through a V-belt. In the passage of air flow, cross section area formed by the valve and cone-shaped contraction part in front of the test section is changed by the valve oscillation. Fig. 1 Test section for temperature measurement and Schlieren visualization Fig. 2 Apparatus of heat transfer experiments 2.000 1.800 0 0.900 1.600 1.400 0.800 0.700 1.200 0 0.600 0.500 0.800 0.600 0.400 0.300 0.400 0.200 0.200 0.100 0.000 0.000 0 90 180 270 360 450 540 630 720 Cam angle [deg] Fig. 3 Design concept of flow rate fluctuation 2

FLOW AND HEAT TRANSFER AROUND THE FLAT PLATE INSTALLED IN A RECTANGULAR DUCT WITH FLOW PULSATION Fig. 4 Optical system layout of color Schlieren method Therefore, cyclic flow rate change was realized with valve motion. Design concept of the flow rate fluctuation is indicated in fig.3. Figure 4 shows the optical system layout of visualization of the temperature field by color Schlieren method. 2.2 Data Reduction This study evaluated heat transfer characteristics in a form of local Nusselt number as the function of three individual parameters expressed as equation (1). Nu( X ) = f ( Rem,Re f, f ) -----------------------(1) In eq.(1), Re m and Re f were mean velocity based and velocity amplitude based Reynolds numbers, respectively and were defined as follows; Rem = u m d e / ν -------------------------------(2) Re = u d / e ν --------------------------------(3) f f 1 Amax Amin uf = ( umax umin ) = u m --------(4) 2 Amin + Amax Subscripts max and min mean maximum and minimum value within the fluctuation, and variable A in eq. (4) indicates the cross sectional area of the contraction part in the pulsation generator. Local heat transfer coefficient and Nusselt number in the case of steady flow was based on the measurements of surface temperature and heat flux and was calculated by equations (5) and (7). h( X ) = q& /( T ( X ) T ( X )) ------------------(5) w b δt(x) δt (X) Fig. 5 Conceptual figure of definition of thermal boundary-layer thickness q& w Tb ( X ) = Tin + X -------- (6) ρ c u A p m cross Nu( X ) = h( X ) d e / λ ------------------------- (7) From the fundamental recognition of convection heat transfer represented in fig.5 and eq. (8) T q& = λ = h( X ) ( Tw ( X ) Tb ( X )) y -(8) y=0 We can also define the thermal boundary-layer thickness and heat transfer coefficient as equations (9) and (10), respectively. ( Tw ( X ) Tb ( X )) δ t ( X ) = ------------------ (9) T y y=0 h( X ) = λ / δ t ( X ) -----------------------------(10) Thermal boundary-layer thickness δ t (X ) for steady flow is able to be calculated from equations (5) and (10). Compared δ t (X ) with the color Schlieren visualization results, color boundary line indicating thermal boundary layer is able to be found on the visualized image. In the case of pulsating flow, local heat transfer coefficients were obtained by eq. (10) based on the measurements of time-averaged δ t (X ) on the time-resolved visualized data of temperature field. Therefore we defined the heat-transferenhancement index and local Nusselt number as equations (11) and (12), respectively. δ t ( X ) steady flow H enh. ( X ) = ---------------(11) δ ( X ) t pulsating flow 3

Hironori Saitoh Nu( X ) pulsating = Nu( X ) steady H enh. ( X ) ----(12) 3. Results (Heat Transfer Experiment) Experiments were carried out within the conditions of 930 Re m 5Hz with constant amplitude as Re f /Re m =0.72. Figure 6 stands for a sample of visualization results of temperature field by color Schlieren method for pulsating flow. For the steady flow case, calculated thermal boundary-layer thickness δ t (X ) from equations (5) and (10) was coincided with inner boundary of red line on the visualized Schlieren image. Heat transfer characteristics were evaluated based on the measurements of the thickness of colored region from the plate surface up to red line in the case of pulsating flow. Monotonous development of thermal boundary-layer on the flat plate is clearly seen for steady flow case in fig.6. On the other hand, for pulsating flow with its frequency of 1Hz, 3Hz and 5Hz, temperature distribution in the near wall region changed with time. Figures 7 (a), (b) and (c) indicate time-resolved data of δ t (X ) in the case of 1Hz, 3Hz and 5Hz, respectively. These three figures have the same abscissa range of one second, therefore, figs. 7 (a), (b) and (c), respectively, correspond to the Yellow Blue Light blue Test section δ Red t (X) X Flow Y Color slit visualized area Steady flow case 1 Hz 3 Hz 5 Hz time Fig. 6 Visualization of temperature field by color Schlieren method (Re m =920) 4

FLOW AND HEAT TRANSFER AROUND THE FLAT PLATE INSTALLED IN A RECTANGULAR DUCT WITH FLOW PULSATION data of one, three and five cycles. It is found that tendency of δ t(x) fluctuation for 1Hz differs from those for 3Hz and 5Hz. This is also noticed in their visualized results (see fig.6). In fig. 7 (a), 1Hz case, fluctuated range in the location of X/X L X/X L =0.05. While for 3Hz and 5Hz cases shown in figs. 7 (b) and (c), qualitative characteristics of δ t (X ) change are similar to each other, however, δ t (X ) in every location for 5Hz case are quantitatively smaller than those for 3Hz case. In spite of these two figures indicate the timeresolved δ t (X ) for three and five cycles, it is clearly seen from these figures that thermal boundary layer fluctuates more than their cycle numbers. Scattering of instantaneous values of δ t (X ) in one second is shown in fig. 8. In the case of 1Hz, fluctuated range increases with X/X L. On the other hand, for 3Hz and 5Hz cases, almost constant range of fluctuation is presented regardless X/X L. Focusing on the effect of pulsating frequency in this figure, we can find that fluctuated range is decreased with increasing of frequency. Figures 9 and 10 show, respectively, timeaveraged local distributions of thermal boundary-layer thickness ( δ t ) and heat transfer enhancement index (H enh ). Based on these two figures local Nusselt number distributions in pulsating flow were obtained and represented in fig. 11. In the case of pulsating flow, Nu(X) was not monotonically decreased with increasing of X/X L. Within the entrance region of X/X L flow pulsation induced 20% decrease in Nusselt number (for 1and 3Hz) or no impact on heat transfer (for 5Hz), compared with steady-flow case. On the contrary, 30 enhancement was indicated in the region of 0.25 X/X L In order to understand such heat transfer characteristics are attributed to what sort of flow behavior, flow visualization was conducted. 3.50 3.00 2.50 2.00 1.50 0.50 0.00 3.50 3.00 2.50 2.00 1.50 0.50 0.00 Re m = 920 Re f / Re m = 0.72 [1Hz] 0.00 0.20 0.40 0.60 0.80 (a) [3Hz] 0.00 0.20 0.40 0.60 0.80 (b) 3.50 3.00 2.50 2.00 1.50 0.50 [5Hz] 0.00 0.00 0.20 0.40 0.60 0.80 time [s] 0.34 0.25 0.15 0.05 0.32 0.25 0.15 0.05 0.32 0.25 0.15 0.05 (c) Fig. 7 Time dependent data of thermal boundarylayer thickness in the cases of pulsating flow [mm] 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 1 Hz 3 Hz 5 Hz 0.000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Fig. 8 Scattering of time-resolved thermal boundary-layer thickness 5

Hironori Saitoh [mm] 3.50 3.00 2.50 2.00 1.50 Re m = 920 Re f / Re m = 0.72 Steady 0.50 1 Hz 5 Hz 0.00 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 4. Results (Flow visualization) 3 Hz Fig. 9 Time-averaged thickness of local thermal boundary layer Figure 12 stands for a general view of the experimental apparatus for flow visualization. Mechanical structure of pulsation generator is the same as one for heat transfer experiments. Water was used as operating fluid and flow was visualized by Hydrogen bubble method. Platinum (Pt) wire was employed as cathode and its layout is shown in fig.13. The test section is recognized as a two-pass duct divided by the flat plate. Straight Pt wire was set in one side of passage, and in the other side corrugated Pt wire was arranged. Supplying continuous direct current to this Pt wire, we simultaneously visualized the both velocity profile and streak line in the duct. Figures 14 (a), (b), (c) and (d) represent the flow visualization results for the cases of 0Hz (steady flow), 1Hz, 3Hz and 5Hz, respectively. In the left side of fig.14 (b), 1Hz case, velocity distribution did not present the typical profile that generally observed in laminar steady flow. It was observed that high and low speed regions alternately existed in span-wise direction, and several pairs of vortices were generated intermediately due to such velocity distribution. This flow instability was also visualized on the streak-line image. Flow pulsation influenced not only bulk flow rate change with time but also the spatial velocity distribution in a moment. 1.60 1.40 1.20 0.80 Re m = 920 Re f / Re m = 0.72 1 Hz 3 Hz 5 Hz 0.60 H enh. (X)= t '(X) steady t '(X) pulsating 0.40 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Fig. 10 Local distributions of heat-transfer enhancement index Re m = 920 80.00 Re f / Re m = 0.72 75.00 70.00 65.00 60.00 Steady 1 Hz 3 Hz 5 Hz 55.00 50.00 45.00 40.00 35.00 30.00 25.00 20.00 15.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Fig. 11 Local Nusselt number distributions Fig. 12 Experimental setup for flow visualization 6

FLOW AND HEAT TRANSFER AROUND THE FLAT PLATE INSTALLED IN A RECTANGULAR DUCT WITH FLOW PULSATION (a) 0Hz : steady flow Fig. 13 Platinum wire layout for Hydrogen bubble method On the other hand, for 3Hz case as shown in fig. 14 (c), flow reversal was occurred near the side walls. As the result of the existence of reverse flow, local flow rate near the flat plate was increased. This phenomenon was confirmed in the visualized image of velocity profile compared with fig. 14 (b). Increase of local flow rate corresponds to stronger shear stress act on the fluid particle in the near flat plate region. This induced relatively large scale vortices, and they were observed in the streak line image. It is clearly understood from the comparison of two figures; fig.14 (c) and (d) that region of flow reversal was increased with increasing of pulsation frequency. (b) 1Hz (c) 3Hz 5. Discussion Heat transfer mechanism in pulsating flow is comprehensible in a comparison of visualization results between flow field and temperature field. For 1Hz case, fluctuation of thermal boundarylayer thickness ( δ t ) near the flat plate is caused by the large scale fluctuation of flow rate. Fluctuation period is almost coincided with pulsation frequency. It can be considered that heat transfer prevention at the entrance region (d) 5Hz Fig. 14 Flow visualization results (Rem=920, Ref/Rem=0.72) 7

Hironori Saitoh for 1Hz and 3Hz cases is attributed to the flow structure with relatively large scale vortices. While for 5Hz case, heat transfer is enhanced because the time-averaged velocity near the flat plate is increased by the flow reversal occurred near the side wall. Change of δ t with time mainly depends on small scale vortices induced by the spatial velocity fluctuation. 6. Conclusions 1. Flow pulsation induces not only bulk flow rate change with time but also the spatial velocity distribution in a moment. 2. Various scales of vortices are generated and flow becomes unstable due to periodical velocity fluctuation in the both meaning of time and space. 3. Heat transfer enhancement or prevention depends on how the velocity fluctuation induces what scale vortices and how such flow instability influences on the large scale of flow pattern. 4. For the correct understanding of pulsating flow structure and its effect on heat transfer, it is necessary to obtain the precise quantitative data of flow field. We will use PIV technique as the next step of this study. Nomenclature A : Cross sectional area [m 2 ] c p : Specific heat at constant pressure [kj/(kg d e : Equivalent diameter [m] f : frequency [Hz] H enh. : Index of heat transfer enhancement [-] h : Heat transfer coefficient [W/(m 2 Nu : Nusselt number [-] q& : Heat flux [W/m 2 ] Re f : Velocity amplitude based Reynolds number [-] Re m : Mean velocity based Reynolds number [-] T b : Bulk air temperature [K] T in : Inlet air temperature [K] T w : Wall temperature [K] : Velocity amplitude [m/s] u f u m : Mean velocity [m/s] w : Width of the flat plate [m] X : Local position in the flow direction [m] Y : Perpendicular direction of X [m] δ t : Thermal boundary-layer thickness [m] λ : Thermal conductivity of air [W/(m ν : Kinematic viscosity of air [m 2 /s] ρ : Density of air [kg/m 3 ] Subscripts b : bulk cross : cross section f : fluctuated in : inlet m : mean max : maximum min : minimum w : wall Acknowledgements The author would like to thank to Mr. N. Kisanuki, Mr. M. Kakiuchi and Mr. K. Mori for their assistance in carrying out the experiments. The author also express a special appreciation to the Japanese ministry of education, culture, sports, science and technology and Japan society for the promotion of science for their money support as grant-in-aid for scientific research. References [1] Niida, T., Yoshida, T., Yamashita, R. and Nakayama, S. The influence of Pulsation on Laminar Heat Transfer in Pipes, Heat Transfer Japan. Res.3, No. 3, pp. 19-28, 1974. [2] Bayley, F. J., Edwards, P. A. and Singh, P. P. The Effect of Flow Pulsation on Heat Transfer by Forced Convection from a Flat Plate, Proc. of the First International Heat Transfer Conference, Boulder, pp. 499-509, 1961. [3] Fujita, N. and Tsubouchi, T., An Experimental Study of Unsteady Heat Transfer from a Flat Plate to an Oscillating Air Flow Heat Transfer Japan. Res.11, pp. 31-43, 1982. [4] Miller, J. A., Heat Transfer in the Oscillating Turbulent Boundary Layer, Journal of Eng. Power, 91, pp.239-244, 1969 [5] Jackson, T. W. and Purdy, K. R., Resonant Pulsating Flow and Convective Heat Transfer, 8

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