See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/276354652 Analysis of Heat Transfer in an Annulus Between Two Horizontal Rotating Cylinders ARTICLE · JANUARY 2009 READS 97 5 AUTHORS, INCLUDING: Reda I. Elghnam Eed Abdel-Hadi Benha University Benha University, Shobra Faculty of Engine… 11 PUBLICATIONS 14 CITATIONS 8 PUBLICATIONS 3 CITATIONS SEE PROFILE SEE PROFILE Available from: Reda I. Elghnam Retrieved on: 27 December 2015 Analysis of Heat Transfer in an Annulus Between Two Horizontal Rotating Cylinders I- Experimental study Reda I. El-Ghnam*, M.G.Mousa**, Eed A. Abdel-Hadi*, Sherief H. Taher*, and Hamed R. Elthan** * Benha University, Shobra Faculty of Engineering ** El-mansora University, Faculty of Engineering Abstract An experimental investigation has been conducted to determine the effects of the rotation, heat flux, eccentricity, and Radius ratio on the convective heat transfer of air between horizontal concentric and eccentric rotating cylinders. An experimental apparatus is designed and constructed to achieve this investigation. The measured data are presented in form of Nusselt number, Rotation Reynolds number, Rayleigh number, eccentricity and Radius ratio. Heat transfer rates (Nusselt numbers) have been computed for Rayleigh number range of 3×103 to 1.6×105, Rotation Reynolds number range of 0 to 820 eccentricity range of 0 to 1.2, aspect ratio range of 29 to 71.5, Radius ratio range of 1.9 to 4.5. This study has explored the thermal behavior in a small gap between the rotating cylinders, and established an empirical formula for the experiment covering the relationship between the parameters of centrifugal force due to rotation, buoyancy force due to temperature difference between inner and outer cylinders, eccentricity and radius ratio with heat transfer coefficient which may be referenced by the designers or engineers in the field of rotating cylinder and components. Comparison with the previous work shows good agreement. Keywords: Mixed Convection, Rotating cylinders, Annulus 1. Introduction The heat transfer in an annulus between two horizontal concentric cylinders have attracted considerable attention because of their wide engineering applications. The study of heat transfer in an annulus has direct industrial applications such as heat exchangers, heat transfer in turbo machineries, indoor climate, double glazed windows, cooling of electrical and electronic components, underground electric transmission cables using pressurized gas and others. Concentric annular pipe flow with rotation of the inner wall is often encountered in engineering applications such as chemical mixing devices, bearings, the drilling of oil wells, Cooling, Rotor-Stator model, Propulsion, Filtration. A rotating annulus is relevant to the co-rotating compressor or turbine disc cavities found in gas turbine engines. Natural convection in eccentric annular space, although not analyzed as extensively, has begun to receive more attention over the last few years. Natural convection heat transfer in eccentric annuli occurs in many industrial situations. Such problems commonly occur within the electric and nuclear energy fields, as well as in solar energy and thermal storage systems. Keyhani et al. [1] conducted experiments with air and helium as a test fluid, when a constant heat flux is applied on the inner wall of the annulus. Takata, et al. [2], have studied numerically and experimentally the natural convection and flow visualization in an inclined cylindrical annulus enclosure. They found that the average Nusselt number slightly increase as the inclination increases, the maximum local Nusselt number at inner and outer cylinder occurs at the inclination angle at 75° and 60°, respectively. Sakr, et al. [3], have studied experimentally and numerically the natural convection in two dimensional region formed by constant flux heated horizontal elliptic tube concentrically located in a -(21)- larger, isothermally cooled horizontal cylinder. The results showed that the average Nusselt number increases as the orientation angle of the elliptic cylinder increases from 0o (the major axis is horizontal) to 90o (the major axis is vertical) and with Rayleigh number as well. Batra [4], and Yoo [5], have investigated the flow characteristics of the fluid in the annular space between two coaxial cylinders with rotating outer cylinder. For the steady flow condition, the velocity distribution and pressure coefficient have been obtained for various values of aspect ratio. Overall heat transfer at the wall is rapidly decreased, as Reynolds number approaches the transitional Reynolds number between two cylinders. Bohn et al. [6-8] have studied computationally and experimentally the free convective heat transfer in sealed air filled rotating annulus. They correlated the experimental data as: 0.213 𝑁𝑢 = 0.365 𝑅𝑎𝜑 𝑓𝑜𝑟 2 × 108 ≤ 𝑅𝑎_𝜑 ≤ 10^10 Bello-Ochende and Adegun [9, 10] have investigated numerically the laminar mixed convective and radiative heat transfer in a tilted, rotating, uniformly heated square and rectangular duct with a centered circular cylinder. The results indicate that the rotation enhances heat transfer but there is tendency that the fluid flow transits into turbulence with low value of Reynolds number if the rotational Reynolds number goes beyond 200. The effect of radiation is only significant for low values of Reynolds number. Ball et al. [11] have studied experimentally the heat transfer in a vertical annulus with rotating and heated inner cylinder while outer cylinder is stationary and cold. They correlated the heat transfer rate as a function of the rotation Reynolds number and radius ratio. Sheng, [12], has measured the temperature distributions against different rotational and heat flux, as well as the impact of the rotating number on heat transfer under a co-axial rotating cylinder with the rotating inner cylinder and stationary outer cylinder. They found that, for the case of rotation of the inner cylinder, the heat transfer of the flow field will increase with the rising rotational Reynolds number under the interaction of the centrifugal buoyancy force. The empirical equation deducted from the experimental results is as: 𝑁𝑢 = 8.854 Pr 0.4 𝑅𝑒Ω0.262 Kuehn and Goldstein [13], have studied experimentally the influence of eccentricity and Rayleigh number on natural convection heat transfer through a fluid boundary by two horizontal isothermal cylinders. Eccentricity of the inner cylinder substantially alters the local heat transfer on both cylinders, but the overall heat transfer coefficient change by less than 10% over the range of eccentricities, maximum occurs at ε/L ≤ 0.66 at the same Rayleigh number. Hosseini [14], has investigated experimentally the natural convection in an open-ended vertical annulus. The results indicate that the rate of heat transfer was greater for eccentric pipes in comparison with the concentric and single pipes. In an eccentric vertical annulus by increasing the eccentric ratios up to 0.5, the rate of heat transfer starts increasing. Around eccentric ratios 0.5–0.7, the heat transfer coefficient almost remains constant. An optimum eccentric ratio, for which the heat transfer rate is maximums, occurs at eccentric ratio 0.5. For eccentric ratios greater than 0.7, the heat transfer rate decrease and becomes minimum at the ratio 1. Nouri and Whitelaw [15], have studied experimentally the flow of Newtonian and nonNewtonian fluids in an eccentric annulus with rotation of the inner cylinder. The results show that the rotation had similar effects on the Newtonian and non-Newtonian fluids. The flow resistance of both fluids increased with rotation at low Reynolds numbers and reduced with increasing values to become similar to those of non-rotating flows. 2. Experimental Test- Rig In this section the experimental facilities, the instrumentations and equipment used throughout this investigation are described. -(22)- The objective of the present study is to investigate experimentally the effects of rotation and eccentricity of inner cylinder on heat transfer characteristics in a horizontal annulus induced due to the rotation of inner cylinder. So, an experimental test rig is designed and constructed for measuring the effect of rotation and eccentricity on the heat transfer coefficient in the annulus. As shown in figure (1) the experimental set-up consists of four main components as: a) Test section b) Rotating unit c) Electric circuit d) The Connecting Unit Each of these subsystems will be described below. 2-1 Test section The test section is designed for the purpose of measuring the heat transfer coefficient from the rotating inner cylinder to the fluid in the annulus. As shown in Fig. (1), the test section consisted of two concentric cylinders; rotating inner cylinder and stationary outer cylinder. The rotating inner cylinder is made from brass while the stationary outer cylinder is made from steel. In the present study two inner cylinders with different outer diameters of 19 and 30 mm and two stationary outer cylinders with inner diameters of 50 and 75 mm are used to get different annulus sizes. All cylinders with the same length of 1000 mm. 1 2 15 4 3 5 14 14 6 7 V 2. 5 A 8 9 10 11 12 13 Fig (1) layout of test rig 1- Wooden Holder 5- Pulley And Belt 9- Stabilizer 13- Motor 2- Test Section 6- Voltammeter 10- Autotransformer 14- Steel Table 3- Sleeve 7- Ammeter 11- Multipoint Switch 15- Connecting Unit -(23)- 4- House Bearing 8- Strobe Scope 12-Temperature Recorder The inner cylinder is heated at constant heat flux by an electric heating element inside it. The electric heating element is constructed using nickel chrome wire which is covered with a sheet of mica to avoid the electric contact between the heater external surface and the inner surface of the rotated brass cylinder as shown in Fig (2). 1- Plug Teflon 2- outer cylinder 3- heater 4- inner cylinder 5- mica sheet Fig (2) Test section Twenty four thermocouple of type-K are used to measure the surface temperatures of both inner and outer cylinder. Twelve thermocouples are imbedded within the surface of each cylinder at equal space. Locations of the thermocouple probes are shown in Fig.(3). The two ends of inner cylinder are sealed with two Teflon bulges to minimize the conduction heat loss from the ends. In order to check the axial conduction heat loss along the cylinder wall, four additional thermocouple probes are embedded in the Teflon inner cylinder ends with 5 mm apart. In addition one thermocouple is used to measure the ambient room temperature. a) at the middle b) at the left end c) at the right end Fig (3) Location of thermocouples on the cylinder surface The cylinders are mounted horizontally on the steel table. The inner rotating cylinder is rotated about its axis and is supported by three houses bearing, as shown in Fig (1). The eccentricity is made by moving the outer cylinder. 2-2 Rotating mechanism A rotating mechanism is used to rotate the inner rotating cylinder with different rotation speeds. The inner cylinder was driven by a 1/2 Hp AC motor and a V-type dual-groove belt pulley system as shown in Fig (1). The rotational speed of the inner cylinder is controlled by changing the -(24)- driving pulley diameter. The velocity of the inner cylinder is measured by a digital strobe scope. Also a tachometer is used to confirm the measurements. The motor is fixed on the other steel frame, to avoid transfer of the vibration from motor to test section during operation. 2-3 Electric circuit The main electric circuit consists of two sub circuits, heater circuit, and motor circuit. The heater circuit consists of 220 AC power supply, auto transformer, analog voltmeter and digital ammeter. A stabilizer is used in the circuit to minimize the voltage fluctuation during experiments. The input electric power to the inner cylinder is controlled by means of a voltage regulator to adjust the voltage drop across the heater terminals. The total power supplied to the heater is determined by recording the values of voltage drop and the current supplied. The motor circuit consists of 1/2 hp motor, AC power supply and stabilizer. The motor has five rotation speeds each of which can divided to different speeds. 2.4 The Connecting Unit Figure (4) shows the details of the connecting unit. The connecting unit is used to supply the power from fixed source to the rotating cylinder and also used to connect the thermocouples which rotate with rotating heated cylinder with the fixed measuring apparatus. The connecting unit consists of a wooden shaft. The shaft has two large grooves one of the two grooves is used to put the power cables inside and the other to put thermocouples wires in. The shaft is mounted on two ball bearings and rotates with the same speed of the inner cylinder. 1- Thermocouple 2- Copper ring 3- Teflon ring 4- Wood rod 5- Multi point switch 6- Temperature recorder Fig (4) Connection between thermocouples and temperature recorder Thirty one copper rings are fixed on the wooden shaft. All copper rings are completely isolated from each other using Teflon rings. Twenty nine of the rings is used to connect the thermocouple ends -(25)- to temperature measuring unit and the other two rings are used to connect the power cables from the heater to power supply. Thirty one carbon brushes are used to connect the rotating copper rings with the fixed measuring units and power supply. Each carbon brush is mounted in a spring and the springs are isolated from each other. 3. Results and discussions In the present experimental study, analysis of heat transfer in an annulus between two horizontal rotating cylinders is investigated. Overall heat transfer coefficient in the form of average Nusselt number are introduced. Firstly, the experimental results are verified by comparing them with the existing data of stationary concentric annulus and also in order to determine the reliability of the present test rig. Figure (5) shows a comparison between present experimental data and that obtained by the available published references, Keyhani [1] and Davies [16]. The figure shows the effect of variation of Rayleigh number on average Nusselt number for different values Radius ratios for stationary concentric annulus. It is observed that the present experimental results are in good agreement with the available data from previous work. The present results can be correlated as: ̅̅̅̅ 𝑁𝑢 = 0.668 𝑅𝑎0.27 𝐴𝑆 −0.264 𝑅 0.14 While the correlations given by both Keyhani [1] and Davies [16] are: ̅̅̅̅ 𝑁𝑢 = 0.291 𝑅𝑎0.322 𝐴𝑆 −0.238 𝑅 0.442 [𝐾𝑒𝑦ℎ𝑎𝑛𝑖] ̅̅̅̅ 𝑁𝑢 = 0.3325 𝑅𝑎0.3 𝐴𝑆 −0.25 𝑅0.442 [𝐷𝑎𝑣𝑖𝑠] 10 14 present 10 present Keyhant Average Nusselt number Average Nusselt number 12 Sherif 8 6 4 8 Keyhani Davies 6 4 2 2 As= 34.5, R= 2.9 As=29, R= 4.63 0 0 1.0E+03 1.0E+04 1.0E+05 1.0E+03 1.0E+06 1.0E+04 Raeiylgh number 8 6 presenlt Davies Keyhent Average Nusselt number Average Nusselt number present Davies 4 2 6 Keyhent 4 2 As= 51.4,R= 3.1 As=71.4, R=1.94 0 0 1.0E+03 1.0E+05 Rayliegh number 1.0E+04 1.0E+05 1.0E+03 1.0E+04 1.0E+05 Rayliegh number Rayliegh number Figure (5) a comparison between present experimental data and that obtained by the available published references, Keyhani [1] and Davies [16]at different values of aspect ratios (AS) and Radius ratios (R) for stationary concentric annulus For rotating annulus, experimental results are carried out for Rayleigh number (Ra) in the range of 3103 to 1.6 105, Rotation Reynolds number (ReΩ) varied from 0 to 820, eccentric ratio (ε) varied from 0 to 0.8 and radius ratio (R) varied from 1.93 to 4.5. For rotating annulus, there are two -(26)- influential factors for centrifugal buoyancy force: one is the centrifugal force triggered by rotation, the other one is the buoyancy effect arising from the temperature difference between the inner and outer cylinders. In this research, the Rayleigh number for buoyancy force effect and rotational Reynolds number for centrifugal force effect will be the key factors decisive to the inner thermal behavior of the entire rotating annulus. 16 25 eccentricity ratio=0.24 14 Eccentricity ratio=0.083 20 12 15 Nu Nu 10 8 10 6 4 2 Ra=32000 Ra=45000 Ra=65000 Ra=10200 5 Ra=82000 Ra=45000 Ra=65000 Ra=82000 Ra=10200 0 0 0 100 200 300 400 500 0 100 200 300 400 500 Re Re 25 20 18 16 14 12 10 8 6 4 2 0 eccentricity ratio=0.32 eccentricity ratio=0.167 20 15 Nu Nu Ra=32000 10 Ra=32000 Ra=45000 Ra=65000 Ra=82000 5 Ra=10200 Ra=32000 Ra=45000 Ra=65000 Ra=82000 Ra=10200 0 0 100 200 300 400 500 0 Re 100 200 300 400 500 Re Figure(6 ) Effect of variation of Reynolds number Re on average Nusselt number Nu for Radius ratio=1.933 and different values of Rayleigh number Ra and one eccentricity ratio ε The influence of the Rotation Reynolds number (ReΩ) of the eccentric annulus on the average Nusselt number ( Nu ) at various amplitudes of Rayleigh number (Ra) and eccentric ratio (ε) at constant Radius ratio values of 1.93 are shown in Fig (6). This figure shows that the average Nusselt number ( Nu ) increases with the increase of (ReΩ) at constant eccentric ratio, Radius ratio and Rayleigh number The influence of the variation of Rayleigh number on the average Nusselt number at constant Radius ratio equal 2.84 and different values of the Rotation Reynolds's number is shown in Fig.(7). These figures show that the average Nusselt number ( Nu ) increases with the increase Rayleigh number at constant Rotation Reynolds's number and eccentric ratio. Rayleigh number provides a measure of the significance of the buoyancy force. For increase Rayleigh number the effect of buoyancy force increase and temperature difference increase. The increase of temperature difference increases the circulation and in turn heat transfer rate increases. Fig.(8) shows the effect of the eccentric ratio of the rotating eccentric annulus on the average Nusselt number at various amplitudes of rotational Reynolds number at radius ratio equal to 4.5. This -(27)- 12 16 eccentricity ratio=0.48 eccentricity ratio=0.16 10 14 12 10 Nu Nu 8 6 2 4.E+04 6.E+04 8.E+04 Re=0 Re=114 Re=228 Re=342 Re=456 4 2 0 2.E+04 8 6 Re=0 Re=114 Re=228 Re=342 Re=456 4 0 2.E+04 1.E+05 4.E+04 6.E+04 Ra Ra 1.E+05 16 16 eccentricity ratio=0.32 14 12 12 10 10 Nu 14 Nu 8.E+04 8 6 2 0 2.E+04 4.E+04 6.E+04 8.E+04 8 6 Re=0 Re=114 Re=228 Re=342 Re=456 4 eccentricity ratio=0.64 Re=0 Re=114 Re=228 Re=342 Re=456 4 2 0 2.E+04 1.E+05 4.E+04 6.E+04 Ra 8.E+04 1.E+05 Ra Figure( 7) Effect of variation of Rayleigh number Ra on average Nusselt number Nu for Radius ratio=2.84 and different values of Reynolds number Re and one eccentricity ratio ε 7 6 12 Rayliegh number=22000 Rayleigh number=5200 10 5 Nu Nu 8 4 3 2 1 Re=0 Re=61 Re=112 Re=264 6 4 2 Re=198 0.20 0.40 0.60 0.80 1.00 0 0.00 1.20 Eccentric ratio 9 Rayliegh number=12000 8 8 7 7 6 6 5 5 Nu Nu 9 4 3 Re=0 Re=61 2 Re=112 Re=264 1 Re=198 0 0.00 Re=61 Re=112 Re=264 Re=198 0 0.00 Re=0 0.20 0.40 0.60 0.80 Eccentric ratio 1.00 1.20 0.20 0.40 0.60 0.80 Eccentric ratio 1.00 1.20 Rayliegh number=12000 4 3 Re=0 Re=61 2 Re=112 Re=264 1 Re=198 0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 Eccentric ratio Figure( 8) Effect of variation of eccentricity ratio ε on average Nusselt number Nu for Radius ratio=4.5 and different values of Rayleigh number Ra and one Reynolds number Re The effect of angle of eccentricity on the average Nusselt number at constant Radius ratio of 2.8 and constant eccentric ratio of 0.34 is shown in Fig. (9). The variation is almost -(28)sinusoidal and similar behaviour is noticed with maximum value occurring at angle of 67 o and minimum value at angle of 0.0 o. It is also noticed that the average Nusselt number figure shows that the average Nusselt number ( Nu ) increases with the increase eccentric ratio at constant rotation Reynolds's number and Rayleigh number. The eccentricity causes an increase in cross-section area in one side and reduction in the cross-section area in opposite side (in eccentric direction). So the circulation increases in wide side and temperature gradient increases in narrow side and both increase the heat transfer rate. The figure demonstrates that the average Nusselt number ( Nu ) increases linearly with the increase of eccentricity ratio for the same Rotation Reynolds's number and Rayleigh number. The effect of angle of eccentricity on the average Nusselt number at constant Radius ratio of 2.8 and constant eccentric ratio of 0.34 is shown in Fig. (9). The variation is almost sinusoidal and similar behaviour is noticed with maximum value occurring at angle of 67 o and minimum value at angle of 0.0 o. It is also noticed that the average Nusselt number increases with the increase in the Rotation Reynolds number for all angles. Fig.(9) Variation of average Nusselt number (Nu) with angle of eccentricity(θ) for different values of rational Reynolds number (ReΩ). at Ra=32000, R=2.8 and ε=0.34 An empirical correlation is deduced here to fit the present experimental results which correlate the average Nusselt number, Rayleigh number, rotational Reynolds number, Aspect ratio, Radius ratio and eccentricity using the Statistical Package for Social Science (SPSS) program. This equation is given by: ̅̅̅̅ = 0.714 𝑅𝑎0.27 𝐴𝑠 0.264 𝑅 0.14 (1 + 0.002 𝑅𝑒Ω0.98 )(1 + 0.1623 𝜀) 𝑁𝑢 The experimental measurements fit this correlation with ± 9 % maximum deviation, as shown in Fig. (10). -(29)- 4 Comparison between Present Results and Published data Figure (11) shows a comparison between the present experimental results and that of Bohn [6] using air as a working medium. It is observed from this figure that the comparison shows a good agreement. ±9% Average Nusselt number Average Nusselt number Fig. (10) the measured average Nusselt number versus calculated average Nusselt number Rayleigh number Ra Rayleigh number Ra Fig. (11) a comparison between the present experimental results and that of Bohn [6] using air as a working medium -(30)- 5- Conclusions The present study is concerned with the convection heat transfer in the horizontal circular annulus between two cylinders. The outer cylinder is fixed while inner cylinder is rotating. Two cases are considered concentric and eccentric annulus. Air is considered here as a working fluid which is filling the annulus. The heat transfer due to the rotation and eccentricity of the inner cylinder has been studied experimentally. A test rig is built to measure the temperatures and hence calculates the average heat transfer coefficient under various rotation and eccentric conditions. The main conclusions drawn from the present study are summarized as follows: 1) This study has explored the thermal behavior in a small gap between the rotating cylinders, and established an empirical formula for the experiment covering the relationship between the parameters of centrifugal force due to rotation, buoyancy force due to temperature difference between inner and outer cylinders, eccentricity and radius ratio with heat transfer coefficient which may be referenced by the designers or engineers in the field of rotating cylinder and components. The present experimental results fit the deduced correlation that relates the average Nusselt number, Rayleigh number, rotational Reynolds number, Aspect ratio, Radii ratio and eccentricity as: ̅̅̅̅ 𝑁𝑢 = 0.714 𝑅𝑎0.27 𝐴𝑠 0.264 𝑅 0.14 (1 + 0.002 𝑅𝑒Ω0.98 )(1 + 0.1623 𝜀) 2) The experimental results compare favorably with the available literature data. 3) The average Nusselt number has a strong dependence on the rotational Reynolds number and the Rayleigh number. The average heat transfer coefficient increases with the increase of rotational Reynolds number and Raleigh number. The rate of heat transfer is greater for eccentric annulus in comparison with the concentric annulus. 4) For high Raleigh number the rotational Reynolds number has minimum effect on the average heat transfer coefficient. 5) The average heat transfer coefficient increases with the angle of eccentricity and has it maximum value at angle of 60o. Nomenclature A area As Aspect ratio, L/D D gap between the inner and outer cylinder, (do- di)/2 di Outer diameter of inner cylinder do Inner diameter of outer cylinder e displacement of inner-cylinder axis from outer-cylinder axis g Acceleration due to gravity heat transfer coefficient, h q h (Ti To ) Kf L N Nu q R thermal conductivity of fluid Length of cylinder (height of annulus) Revolution per minuet Nusselt number, Nu = hdi / Kf wall heat flux per unit area Radius ratio(do/di) Ra Rayleigh number Ra g (Ti To )d i 3 -(31)- ReΩ T Rotational Reynolds number, ReΩ = Ωdidi/ ν temperature Greek letters α thermal diffusivity β coefficient of thermal expansion ν kinematic viscosity 2N Angular velocity, = Ω 60 2 e Eccentric ratio, ε (di ) ρ Fluid density Subscript f o i b fluid Outer cylinder Inner cylinder bulk References 1 Keyhani, M., Kulacki, F. A., and Christensen, R. 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R., and Hatam, M., (2005) "An experimental study of heat transfer in an open-ended vertical eccentric annulus with insulated and constant heat flux boundaries", Applied Thermal Engineering, vol. 25, pp. 1247–1257 Nouri J. M and. Whitelaw, J. H (1997), "Flow of Newtonian and non-Newtonian fluids in an eccentric annulus with rotation of the inner cylinder", J. Heat and Fluid Flow vol. 18, pp. 236-246. de Vahl Davis, G., and Thomas, R. W., (1969), " Natural convection between concentric vertical cylinder", High speed computing in fluid dynamics, physics of fluid, supplement II, pp. 198-207. -(33)-