Experimental Study on Heat Transfer Augmentation for High Heat Flux Removal in Rib-Roughened Narrow Channels

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 35, No. 9, p. 671-678 (September 1998) TECHNICAL REPORT Experimental Study on Heat Transfer Augmentation for High Heat Flux Removal in Rib-Roughened Narrow Channels Md. Shafiqul ISLAM*, Ryutaro HINO**,t, Katsuhiro HAGA**, Masanori MONDE* and Yukio SUDO** * Mechanical Engineering De partment, Saga University ** Tokai Research Establishment, Japan Atomic Energy Research Institute (Received January 21, 1998) Frictional pressure drop and heat transfer performance in a very narrow rectangular channel having onesided constant heat flux and repeated-ribs were studied experimentally for turbulent water flows. Their empirical correlations were derived for designing target cooling channels to remove high heat flux generated at target plates in a high-intensity proton accelerator system. The rib pitch-to-height ratios (p/k) were 10 and 20 while holding the rib height constant at 0.2mm, the Reynolds number (Re) from 2,400 to 98,500 under different channel heights (H) of 1.2mm and 3.2mm, the rib height-to-channel equivalent diameter ratio (k/de) of 0.088 and 0.036, respectively. The results show that the rib-roughened surface augments heat transfer by about 2-2.5 times compared with the smooth surface at the expense of around 2.5 times higher frictional pressure drop under a range of Re=8, 000-to-30,000 at p/k=10, and H=1.2mm. Experimental results of channel height, H=1.2mm show slightly higher heat transfer and friction factor performance than that of the channel height, H=3.2mm. KEYWORDS: pressure drop, heat transfer, augmentation, narrow channel, repeated ribs, empirical correlation, heat flux, target plate, pressure dependence I. Introduction In the 21st century, neutron is expected to play a very important role in fields such as structural biology, nuclear physics and material science if a very high-intensity neutron source can be built. This is because of its superior nature as a probe to investigate material structure and its function. The Japan Atomic Energy Research Institute (JAERI) has launched the Neutron Science Project for the construction and for the utilization of a high-intensity spallation neutron source, coupled together with a MW-class pulsed proton accelerator. In the project, development of a MW-class spallation neutron source is one of the most difficult technical challenges. A solid target consisting of heavy metal plates such as tungsten and tantalum is to be installed as the spallation neutron source in an early stage of operation under 1.5MW of proton beam power (1.5GeV, 1mA). Through a spallation reaction by a pulsed proton beam with 1ms pulse length at 50Hz to target plates, highdensity heat of up to 4kW/cc under the Gaussian beam profile of 2cm of the half width in radial direction will * H onjo-cho, Saga-shi 840-8502. Tokai-mura, Naka-gun, ** Ibaraki-ken 319-1195. Corresponding author, Tel. +81-29-282-6424, Fax. +81-29-282-5579, E-mail: hino@cat.tokai.jaeri.go.jp be generated at target plates. Then, heat flux reaches up to 10MW/m2 even in the case of the thin target plate of 5mm, so that it is necessary to remove this high heat flux efficiently using water flowing through the cooling channels between the target plates, whose gaps are approximately 1mm due to the fact that decreased water volume leads to decreased neutron absorption(1). In designing the target, heat transfer augmentation using micro repeated ribs working as turbulent promotors was focused on in order to remove high heat flux so as to keep the temperature of the target plates below 200dc using a relatively low velocity. Another important subject to be considered in the structural design of the solid target is the issue that decreased flow velocity may suppress the deviation of the flow rate distribution of the assembled parallel cooling channels. Many of the studies on surface roughness with repeated-ribs have tried to extend the studies of Nikuradse(2) on friction with sand-grain roughness and the heat transfer-momentum transfer analogy of Dipprey and Sabersky(3) for this type of roughness, while Gee and Webb(4) proposed correlations for helical ribs, without including the effects of the pitch. The most general correlations to date were proposed by Withers(5)(6), Li et al.(7), and Nakayama et al.(8) for helically ribbed tubes. Han et al.(9)-(11) systematically determined the effects 671

672 M. S. ISLAM et at of a rib pitch-to-height ratio (p/k) and a rib height-toequivalent diameter ratio (k/de) in relation with a rib angle-of-attack on the heat transfer coefficient and the friction factor of fully developed turbulent air flow in ducts that had two or four rib-roughened walls on opposite sides. Liou et al.(12) also presented the simplest correlations to see the effects of rib shapes on turbulent heat transfer and friction in a rectangular channel. The Webb et al. correlations(13) are those that are applicable to water, air and n-butyle alcohol for transverse repeated-ribs under a wide range of the Reynolds number (Re), rectangular rib geometries and p/k ratios in tubes. These correlations seem to be reliable, taken as a reference for the case of a narrow rectangular channel and then, compared and contrasted with the current study. While many studies on heat transfer augmentation using repeated ribs have been carried out both analytically and experimentally on tubes and annuli under air-flow conditions, very few studies are on rectangular channels under water-flow conditions, so that there is virtually almost no heat transfer data available both analytically and experimentally on a very narrow rectangular channel with repeated-ribs under water-flow conditions. The objective of this study is to determine the effect of repeated-ribs on heat transfer and pressure drop in very narrow rectangular channels in the fully developed turbulent flow regime to clarify the effectiveness of high heat flux removal from the solid targets by heat transfer augmentation. This paper presents the effects of rib height, rib pitch and channel height on heat transfer coefficients and friction factors over a wide range of Re for the very narrow rectangular channels. Six narrow rectangular channels were tested where two of them were smooth (no rib) and the remaining four were rib-roughened from one side. The p/k ratio were 10 and 20 while keeping the rib height and width constant at 0.2mm, Re from 2,400 to 98,500 under different channel heights of 1.2mm and 3.2mm, k/de of 0.088 and 0.036, respectively. II. Experimental Program 1. Test Apparatus The layout of the experimental apparatus and the measuring equipment is shown in Fig. 1. The closedlooped system incorporates a test section, flow meters, a water tank, a water pump, a direct current (DC) power supplier etc. Working fluid (water) from the pump was supplied to the test section through the flow meter, and then, it passed through a filter, a cooler, the water tank and a pre-heater to the pump. The filter was used to filter out solid particles more than 5 that may have found their way into the system. The pre-heater was employed to control the temperature of the water in the test section. The water tank served as a container into which water from the test section was discharged, conditioned, and recirculated. The flow rate through the test section was measured using two electromagnetic flow meters in Fig. 1 Schematic diagram of test apparatus parallel and was controlled by pumping power with an inverter. Inlet pressure was adjusted with a valve installed at the outlet of the test section. The test section shown in Fig. 2 was 250mm in flow length and 200mm in heated length; entry and exit sections of 25mm-long were provided to obtain a smooth flow. The test section consists of a heating surface made of copper plate with an electric heater, glass windows etc. A12O3 blocks were used as insulting materials to minimize heat loss from the heated surface. A nichrome plate (0.905O/m) was used as a heater and received electricity of up to 120A and 17V from the DC power supplier. The total heat input to the heating surface was calculated from the current and the voltage across the heating surface, which were measured by a precision ammeter and a voltmeter, respectively. The ribs were produced by machining the surfaces of the heating plates with a NC machine tool, whose cross-sectional dimension was 0.2mmx0.2mm and with rib pitches of 2 or 4mm, respectively. Square ribs were employed as they reveal the better heat transfer performance than that of the triangular or semicircular ribs since the flow does not travel smoothly over square ribs and square crosssectional blockage accentuates inertial losses(12). The width of the rib roughened surface was 20mm and the channel heights was varied between 1.2mm and 3.2mm. The heights were measured by a digital microscope and rechecked by an ultrasonic method. The major parameters and experimental conditions of the flow channel are presented in Table 1. Surface temperature was measured at 26 points along the centerline and 2mm (LIZ) away from the heating surface, and was recorded by the data acquisition system consisting of a data logger JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Heat Transfer Augmentation in Rib-Roughened Narrow Channels 673 Table 2 Experimental conditions D P=4fDL/De,rv2/2g. (1) The friction factor, f, is based on an unheated test section. The present friction factor was compared with that for fully developed turbulent flow in smooth rectangular channels, fs, by means of the Blasius correlation: Fig. 2 Schematic drawing of test apparatus Table 1 Major parameters of flow channel and a personal computer. The distance between the two consecutive thermocouples was 8mm. Three thermocouples each at the inlet and the outlet of the test section were provided outside of the heated region to measure the inlet and the outlet bulk temperatures of water. Eleven differential pressure taps were installed at the opposite side of the heating surface to measure the static pressure drop across the test section. The distance between the two consecutive pressure taps was 20mm. The experimental conditions under which the data were obtained are listed in Table 2. 2. Data Analysis The friction factor in a rib-roughened narrow rectangular channel can be determined by measuring the pressure drop across the test section and the flow rate of the water. The friction factor can then be evaluated from: f/fs=f/(0.079re-0.25). (2) Heat input was calculated from the DC power supplier as follows: Q=IV. (3) The heat input coincides well with the increase in enthalpy calculated by Eq. (4). The average inlet and outlet temperatures of the water, Tin, Tout, were used in Eq. (4) to obtain heat transfer rate. The average inlet and outlet temperatures of the water were obtained by averaging three thermocouples located at the inlet and outlet of the test section. The net heat transfer rate can be calculated from: Q=CprvA(Tout-Tin). (4) The local heat transfer coefficient was calculated from the net heat transfer rate per unit surface area to water, the corrected surface temperature, Twc on each measured section, and local bulk water temperature, Tb, as: h=q/s(twc-tb), (5) where the local temperature, Tw, was read from each thermocouple output. The corrected local surface temperature, Twc, was calculated by one dimensional steady state heat conduction equation as: lwpt/p ZDZ=Q (6) Twc=Tw-(Qd)/(Slw), (7) where axial and span wise heat conductions were not considered in this study. The surface area, S (=LW) was based on the smooth surface area, not including an increase in the surface area due to ribs; increment of the surface area is 17% at p/k=10 and 8.5% at p/k=20, respectively. Equation (5) was used for both the ribroughened surface and the smooth surface heat transfer coefficient calculations. The local inner wall tempera- VOL. 35, NO. 9, SEPTEMBER 1998

674 M. S. ISLAM et al. ture, Tẉ was at maximum 23dc in the fully developed flow region for the case of a smooth surface (no ribs) at low Re while channel height, H=1.2mm. The inlet water temperature was at best 15dc depending on the test conditions. The local bulk water temperature, Tb, was calculated assuming a linear water temperature rise along the flow channel and defined as: Tb=Tin+(Tout-Tin)X/L. (8) The local Nusselt number, Nu, of the present study was compared with the Nusselt number for fully developed turbulent flow on smooth surfaces correlated by the Dittus-Boelter, Nus, as: Nu/Nus=QDe/{Sl(Twc-Tb)}/0.023Re0.8Pr0.4. (9) For the case of non-heating and heating experiments, errors in the reduced data of pressure drop, Re, flow rate and heat transfer coefficient are determined using the following measurement uncertainties: water flow rate +2.5%, differential pressure gauge accuracy +0.2%, thermocouple accuracy +0.4%, voltmeter accuracy +0.4%, ammeter accuracy +-0.5%. III. Results and Discussion 1. Frictional Pressure Drop Performance Most of the experimental data using water, air etc. as a working fluid show negligible effects on Re in the fully turbulent flow for tubes or channels with surface roughness. Citings of such type of experiments are Han et al.(10), Liou et al.(12), Webb et al.(13) etc. For the rib-roughened surface, p/k ratio plays a predominant role to increase the friction factor for turbulent flows. Figures 3(a) and (b) compare the friction factor with the smooth surface along with prediction and experimental results at different channel heights. The smooth surface friction data agree well with the Blasius correlation. The dashed lines show the predictions that were calculated by following Webb et al. correlation(13), which is applicable to water and air: (2/f)0.5=2.5ln(De/2k)-3.75+0.95(p/k)0.53. (10) From Eq. (10), as it is no longer dominated by shear but by the drag forces on the roughness elements, it is seen that the friction factor is independent of the Re in the fully rough regime, k+>=35, where k+(=u*k/v, u*: friction velocity) is the roughness Reynolds number. Equation (10) is applicable within p/k ratios of 10 to 40(13). The experimental friction data of rib-roughened surface is over predicted by about 8 times lower than that predicted at p/k=10, Re=104 and H=1.2mm by using Eq. (10) where experimental results are 2.25 times higher than that of the smooth surface. It can be seen that the experimental values of friction factors strongly depend on Re and decrease with increasing Re and p/k ratios. The highest friction factor is obtained at p/k=10 within the range of p/k between 10 and 20. higher channel height for example, H=3.2mm may Fig. 3 Comparison of friction correlation with Webb et al. not contribute to high frictional pressure drops. It is obvious, however, that the roughness increases the friction factor at the expense of frictional pressure drop along the flow direction. The laminar flow is confined to occurances at Re<=2,000. The transition character from laminar to turbulent flows occurs in 2,000<=Re<8,000 and the fully de- JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Heat Transfer Augmentation in Rib-Roughened Narrow Channels 675 veloped turbulent flow occurs in the region of Re>=8,000. The solid lines passing through the data points are the least-square fits shown as follows: f=0.272re-0.29; p/k=-10, H=1.2mm (11) f=0.205re-0.29; p/k=20, H=1.2mm (12) p/k=10, H=3.2mm (13) f=0.049re-0.11; f=0.044re-0.11; p/k=20, H=3.2mm. (14) The maximum scatters of the data points relative to Eqs. (11) to (14) are within +-1.2, +-1.3%, +-3 and +-2%, respectively. From these equations, the turbulent flow would appear at Re<8,000 in the rib-roughened narrow channel. The general correlation is obtained from Eqs. (11)- (14) within limited ranges of p/k ratios for the case of a narrow channel and is expressed by (15) This correlation is valid within p/k ratios from 10-to- 20 and k/de ratios from 0.036-to-0.088, under a wide range of Re up to 105. Figure 4 shows the comparison of measured data and the predicted results by using Eq. (15). As seen the figure, the maximum scatter of measured data to predicted results is within +-5% and the standard deviation is 2%, respectively. 2. Heat Transfer Performance Figure 5 shows the heat transfer performance for the geometry of k/de=0.088, w/k=1.0 and H=1.2mm with two p/k ratios along with predictions. Measured data shown in the figure were located in the region of X/De where the surface temperature showed the trend of linear increase along the flow direction characterizing the Fig. 5 Comparison of heat transfer correlation with Webb et al. fully developed region. The heat transfer rate measured for the smooth surface is slightly larger than that by the Dittus-Boelter equation. The dashed lines indicate the predictions by the Webb et al. correlation which is expressed by (16) It can be seen that the Webb et al. correlation overpredicts the experimental data. The standard deviation is estimated to be 42 and 44% at p/k=10 and 20, respectively. The rib-roughened surface augments heat transfer by about 2-2.5 times compared with that for the smooth surface at p/k=10 and Re=8,000-to-30,000. In Fig. 5, the solid lines passing through the data points are the least-square fits and the maximum scatter of the data points relative to the least-square lines is within +-15%. The least-square fits are expressed by (17) Fig. 4 Comparison of measured and predicted friction data (18) The highest heat transfer augmentation takes place at p/k=10 and heat transfer rate decreases as the p/k ratio increases. Figure 6 shows the heat transfer performance for the geometry of k/de=0.036, w/k=1.0 and H=3.2mm with two p/k ratios along with prediction. Measured data shown in the figure were in the fully developed region. VOL. 35, NO. 9, SEPTEMBER 1998

676 M. S. ISLAM et al. than at p/k=20. The dependence of the Nusselt number on the rib height, rib pitch, and Re is derived not only from our experimental data but also the Webb et al.'s experimental data obtained under water flow conditions with a rib-roughened tube of 36.83mm in diameter(14). This is expressed in a general form as: Fig. 6 Comparison of heat transfer correlation with Webb et al. The difference between the prediction by the Webb et al. correlation and experimental results was small in the case using a higher channel height, where H=3.2mm. The estimated standard deviation is 31 and 20% at p/k=10 and 20, respectively. From observing the tendency of the experimental data, it can be deduced that heat transfer augmentation will not be effective at Re>105. The discontinuity between the experimental results and the predictions would be owing to the fact that the prediction correlation was obtained with large tubes, 36.83mm in diameter. It is seen from Fig. 6 in comparison with Fig. 5 that higher channel height, H=3.2mm may not play any significant role from the viewpoint of heat transfer augmentation when rib height remains constant. The solid lines passing through the data points are the least-square fits and the maximum scatters of the data points relative to the least-square lines are within +-10 and +-13%, respectively. These are expressed as: (21) The constants vary with k, p, and H. Equation (21) is valid for 10<=p/k<=20, 0.02<=k/De<=0.088, under a wide range of Re up to 105. The comparison of measured and predicted heat transfer rates is shown in Fig. 7. The maximum scatter of predicted data is within +15% and the standard deviation is 6.7%, respectively. Figure 8 shows the relationship between boundary layer thickness and heat transfer augmentation by the ribs. The boundary thickness, y, was estimated with following equation(14): (22) Then. the thickness of the viscous sublayer on the smooth surface, y+, is typically taken to be y+<=5, for the buffer layer regime 5<y+<=40, and for the turbulent flow regime y+>40(14). To augment heat transfer by about 2 times higher than the smooth surface, the rib height is found to be less than 20 and 8 times higher than the viscous sublayer thickness at p/k=10 and 20, respectively. The highest heat transfer augmentation will be expected when the rib height is around 2-3 times higher than the viscous sublayer thickness. From this relationship, the optimum (19) (20) These equations might be extended to low Re regions down to 4,000. It is clear from these two figures that the highest heat transfer augmentation is taking place at p/k=10 for both channel heights and then, the augmentation decreases as the p/k ratio increases. This is physically reasonable since the turbulence intensity on the repeated-rib surface due to boundary layer separation and reattachment between the ribs is higher at p/k=10 Fig. 7 Comparison of measured and predicted heat transfer data JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

Heat Transfer Augmentation in Rib-Roughened Narrow Channels 677 to the design of coolant channels in the solid target, and would be useful for cooling designs of high heat flux components in a fusion reactor such as the first wall. Fig. 8 Relationship between boundary layer thickness and heat transfer augmentation by rib condition of the rib height and the p/k ratio can be predicted for the heat transfer augmentation on the basis of the viscous sublayer thickness on the smooth surface. IV. Concluding Remarks The thermal-hydraulic characteristics of single-phase turbulent flows in narrow rectangular channels with and without repeated-ribs were studied experimentally for the target cooling channels. The friction factor and the heat transfer performance did not match well with the results of previous studies(13)(14). For the flow through a smooth channel, both the measured Nusselt number and friction factor agree well with the Blasius and Dittus- Boelter correlations. The experimental results showed very good heat transfer performance and it is possible to augment heat transfer by about 2-2.5 times compared with the smooth surface in the fully developed region at p/k=10, Re=8,000-to-30,000, H=1.2mm. Friction factor can be a strong function of Re from the transition to the fully developed flow regimes and expected to be an asymptotic value at high Re. The rib height can be predicted by comparing it with the viscous sublayer thickness so as to obtain the heat transfer augmentation prior to the experiments. General correlations in terms of Re, dimensionless rib pitch/height (p/k) ratios and rib height/channel equivalent diameter (k/de) ratios are obtained for both the fully developed friction factor (f) and the Nusselt number (Nu). The correlations of f and Nu are applicable within limited ranges of p/k ratios 10 to 20 and Re up to 105: the friction correlation is valid for 0.036<k/De<0.088 and the heat transfer correlation for 0.02<k/De<0.088. The standard deviations of these correlations, f and No, are 2 and 6.7%, respectively. The results obtained in this experiment can be applied [NOMENCLATURE] A: Flow cross-sectional area Cp: Specific heat at constant pressure D: Tube diameter De: Equivalent diameter, 4(HxW)/2(H+W) f: Friction factor g: Acceleration due to gravity h: Forced convection heat transfer coefficient H: Channel height I: Current k: Rib height k+: Roughness Reynolds number, u*k/v L: Channel length No: Nusselt number, hde/l p: Rib pitch P: Pressure D difference Pr: Prandtl number, Com/l Q: Heat input Re: Reynolds number, vde/n S: Surface area St: Stanton number, Nu/RePr T: Temperature u* : Friction velocity, (tw/r)0.5 v : Fluid velocity V: Voltage w: Rib width W: Channel width X: Local distance along flow direction y: Local distance from the surface y+: Dimensionless distance, yu*/n Z: Local distance in the wall (Greek symbol) n : Fluid kinematic viscosity l : Thermal conductivity r : Fluid density m : Fluid dynamic viscosity t : Shear stress, (DeDP)/4L D : Increment d : Distance from the surface to thermocouple location O : Electric resistance (Subscripts) b: Bulk c: Calculated value m: Measured s: Smooth w: Wall wc: Corrected wall ACKNOWLEDGMENTS This work was performed at Japan Atomic Energy Research Institute. The authors wish to express their sincere gratitude to Mr. Hideki Aita, Mr. Kenji Sekita, and Mr. Katsuo Fujisaki for their assistance in carrying out the experiments. Finally, the authors acknowledge profound indebtness to Dr. M. Z. Hasan, Assoc. Professor of Mechanical Engineering Department at Saga University VOL. 35, NO. 9, SEPTEMBER 1998

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