Experimental investigation of flow resistance and convection heat transfer of CO 2 at supercritical pressures in a vertical porous tube

Transcription

1 J. of Supercritical Fluids 38 (2006) Experimental investigation of flow resistance and convection heat transfer of CO 2 at supercritical pressures in a vertical porous tube Pei-Xue Jiang a,, Run-Fu Shi a, Yi-Jun Xu a,s.he b, J.D. Jackson c a Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing , China b School of Engineering, The Robert Gordon University, Schoolhill, Aberdeen AB10 1FR, UK c Manchester School of Engineering, University of Manchester, Manchester M13 9PL, UK Received 3 July 2005; received in revised form 11 December 2005; accepted 12 December 2005 Abstract Experiments were conducted to measure the convection heat transfer in a vertical porous tube with particle diameters of mm at supercritical pressures. The local heat transfer coefficients, fluid bulk temperatures and wall temperatures were measured to investigate the influence of the inlet fluid temperature, pressure, heat flux and flow direction on the convection heat transfer in the porous tube. The measured friction factors in a heated tube are much larger than those predicted using the Aerov-Tojec correlation for both upward and downward flows. Therefore, two new correlations are presented for upward and for downward flows to predict the friction factors of supercritical pressure CO 2 in heated porous tubes. The experimental results also show that the inlet temperature, pressure and heat flux all significantly influence the convection heat transfer. When the inlet temperature (T 0 ) is higher than the pseudocritical temperature (T pc ), the local heat transfer coefficients are much less than those when the inlet temperature is lower than the pseudocritical temperature. The convection heat transfer coefficients are found to vary nonlinearly with heat flux. For T 0 < T pc, the local heat transfer coefficients along the porous tube have a maximum for upward flow and have a peak value for downward flow when the local fluid bulk temperatures are near T pc and the wall temperatures are slightly higher than T pc. The different variations of the local heat transfer coefficients along the porous tube for upward and downward flows are attributed to the effect of buoyancy. However, when the wall temperatures are much higher than T pc, the local heat transfer coefficients along the porous tube decrease continuously for both upward and downward flows Elsevier B.V. All rights reserved. Keywords: Supercritical fluid; Heat transfer; Porous tube; Carbon dioxide; Experimental investigation; Flow resistance 1. Introduction Supercritical fluids are widely used in many industries such as in power engineering, chemical engineering, aerospace engineering, cryogenics and refrigeration engineering. Investigations of the convection heat transfer of fluids at supercritical pressures in porous media is driven by the need to develop transpiration cooling to protect high temperature surfaces, to develop supercritical fluid extraction technology, and to study the mechanism of hydrogen production during coal pyrolysis. Transpiration cooling is one of the most efficient methods to protect high temperature surfaces such as rocket thrusters and supercritical oxidation equipment used in chemical engineering Corresponding author. Tel.: ; fax: address: Jiangpx@tsinghua.edu.cn (P.-X. Jiang). systems where hydrogen and water at supercritical pressures may be used as coolants flowing through porous walls. In the process of hydrogen production by coal pyrolysis, supercritical water is used as the oxidizer as it flows through the coal packed beds. In the supercritical region, small variations of fluid temperature and pressure cause significant changes of thermophysical properties so that the convection heat transfer of fluids at supercritical pressures has many special features due to the sharp variations of thermophysical properties, especially the variation of c p. The effect of buoyancy in mixed convection can also make a noticeable difference compared to forced convection. Comprehensive research on internal forced and mixed convection heat transfer of supercritical fluids in normal size tubes has been done in the past 50 years by Petukhov [1], Hall [2], Jackson et al. [3,4], Krasnoshchekov and Protopopov [5], Yamagata et al. [6], Protopopov [7], Popov and Valueva [8], Kurganov and /$ see front matter 2005 Elsevier B.V. All rights reserved. doi: /j.supflu

2 340 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) Nomenclature c p specific heat at constant pressure (J/kg K) d tube inner diameter (m) d p particle diameter (m) G mass flow rate (kg/s) Gr Grashof number, Gr = gd 3 ρ(ρ b ρ w )/μ 2 h f,0 inlet specific enthalpy (J/kg) h f,b (x) local fluid bulk enthalpy (J/kg) h x local heat transfer coefficient (W/m 2 K) k thermal conductivity (W/(m K)) M mass flux (=ρu) (kg/(m 2 s)) p pressure (Pa) q w heat flux on the inner tube surface (W/m 2 ) Re Reynolds number Re e equivalent Reynolds number T temperature ( C) or (K) T pc pseudocritical temperature ( C) or (K) u xdirection velocity component (m/s) x axial coordinate (m) Greek symbols ε porosity δ distance from thermocouples to the inner surface (m) μ dynamic viscosity (kg/(m s)) ρ density (kg/m 3 ) Subscripts b bulk dw downward flow f fluid i inner surface s solid wall up upward flow w wall δ outer mini channels of the tube which hold the thermocouples 0 tube inlet Kaptilnyi [9], Jiang et al. [10], and He et al. [11]. Recently, there has been increasing interest in heat transfer research on fluids at supercritical pressures in mini/micro scale tubes or channels with papers by Liao and Zhao [12], Jiang et al. [13] and He et al. [14]. However, to the authors knowledge, there is very limited work on convection heat transfer of supercritical fluids in porous media [13,15,16]. Heat transfer in porous media has received much attention for many years due to its importance in applications such as catalytic and chemical particle beds, solid matrices or microporous heat exchangers, cooling of electronic equipment and mirrors in powerful lasers, phased-array radar systems, industrial furnaces, packed-bed regenerators, combustors, fixed-bed nuclear propulsion systems, micro thrusters, transpiration cooling, spacecraft thermal management systems, and many others. There have been numerous investigations with theoretical analysis, numerical simulations and experimental investigations of convection heat transfer in porous media such as by Vafai and Tien [17], Cheng and Hsu [18], Hunt and Tien [19], Hsu and Cheng [20], Amiri et al. [21], Jeigarnik et al. [22], Achenbach [23], Lage et al. [24], Quintard [25], Jiang et al. [26,27,29], and Alazmi and Vafai [28]. However, all of these studies were for convection heat transfer of normal fluids such as water and air in porous media where the variations of the thermophysical properties with temperature and pressure were not great. Jiang et al. [13] presented some experimental results for convection heat transfer of CO 2 at supercritical pressures in a vertical porous tube only for upward flow with particle diameters of mm. The tests investigated the effects of inlet temperature, mass flow rate, and heat flux on the convection heat transfer in the porous tube. This paper reports new experimental results for both upward and downward flows of CO 2 at supercritical pressures in a vertical porous tube with particle diameters of mm. The tests investigated the effects of inlet temperature, pressure, heat flux, and flow direction on the convection heat transfer and flow resistance. 2. Experimental system and data reducton The experimental system is shown schematically in Fig. 1. The system included a compressed CO 2 container, a cooling water bath and chiller, a high pressure CO 2 pump and a high pressure magnetic pump, an accumulator to eliminate the fluctuation of mass flow rate, a Coriolis mass flow meter, a pre-heater, a test section, an after cooler, manometers, a pressure gauge and a differential pressure gauge, electrical power input and measurement systems, and a data acquisition system (HP 34970A). The test section shown in Fig. 2 was a porous cylindrical tube with inside and outside diameters of 4 and 6 mm and particle diameters of mm. The heated test section length was 50 mm. The porous tube was made of a pure copper tube filled with sintered bronze particles. The porous tube porosity was about 0.4. The test section was heated using electrical resistance wire wrapped around and electrically isolated from the tube. CO 2 flowed into the test section from the bottom to the top for upward flow and from the top to the bottom for downward flow. The parameters measured in the experiments included wall temperatures, inlet and outlet temperatures, mass flow rate, inlet pressure, test section pressure drop, heater voltages, and electrical resistance. The local tube wall temperatures were measured with eight copper-constantan thermocouples inserted into minichannels cut into the test section surface (0.2 mm in depth by 0.2 mm in width) along the tube. Mixers were installed before and after the test section to mix the fluid before the inlet and outlet fluid temperatures were measured by accurate platinum thermal resistance thermometers (RTD). Prior to installation, the thermocouples and the RTDs were calibrated using a constanttemperature oil bath. The accuracies were within ±0.1 C. The inlet pressure was measured using a pressure gage transducer

3 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) Fig. 1. Experimental system. (Model EJA430A) with an accuracy of 0.075% of the full range of 12 MPa. The test section pressure drop was measured using a differential pressure transducer (Model EJA110A) with an accuracy of 0.075% of the full range of 500 kpa. The mass flow rate was measured using a Coriolis-type mass flowmeter (Model MASS2100/MASS6000, MASSFLO, Danfoss). The nominal range of the mass flow meter was 0 65 kg/h with an accuracy of 0.1%. The system required a long time to reach steady state in the experiments (e.g min). The system was determined to be at steady state when the variations of the wall temperatures and the inlet and outlet fluid temperatures were all within ±0.1 C and the variations of the flow rate and the inlet pressure were all within ±0.2% for at least 10 min. The experimental uncertainty of the heat balance was about ±5%. The experimental uncertainty of the convection heat transfer coefficients was mainly caused by experimental errors in the heat balance, axial thermal conduction in the test section, temperature measurement errors and the calculation of the heat transfer surface temperature. The root-mean-square experimental uncertainty of the convection heat transfer coefficient was estimated to be 15.8%. The experimental uncertainties in the inlet pressures were estimated to be ±0.09%. The local temperatures on the inner surface of the porous circular tube were calculated using the measured outer surface temperatures of the tube, T w,δ (x), assuming one-dimensional steady heat conduction in the wall: Fig. 2. Test section schematic. T w,i (x) = T w,δ (x) q wd ln d + 2δ 2k s d (1)

4 342 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) The local heat transfer coefficient, h x, at each axial location was calculated as q w h x = (2) T w,i (x) T f,b (x) The local fluid bulk temperature, T f,b (x), was calculated from the local fluid bulk enthalpy, h f,b (x), using h f,b (x) = h f,0 + q wπ dx (3) G The Reynolds number based on the mean fluid temperature and the particle diameter was defined as Re dp = ρud p μ = 4Gd p πd 2 μ (4) 3. Experimental results and discussion Fig. 3 presents the thermophysical properties of CO 2 at 8.5 MPa calculated by NIST REFPROP Version 7.1 [31]. The pseudocritical temperature, T pc, is 37.4 C for CO 2 at this pressure. The thermophysical properties of CO 2 at supercritical pressures sharply vary with fluid temperature and pressure. The specific heat reaches a maximum at the pseudocritical temperature. Fig. 4. Friction factor for CO 2 at supercritical pressures in the sintered porous tube without heating: p = MPa, T f,b = C, G = kg/h. Figs. 4 and 5 compare the friction factor, f e, calculated from the experimental data for flow of CO 2 at supercritical pressures in the sintered porous media with Eq. (5). The friction factors of CO 2 at supercritical pressures at constant temperature (without 3.1. Flow resistance in the porous tube Previous works [26,29] showed that the friction factor, f e, calculated from the experimental data for normal fluids such as water and air in porous media with enough particles in the crosssection of test section can be well predicted using the equation given by Aerov and Tojec [30]: f e = ε3 m ρ f d p p 1 ε m 3M 2 L = Re e (for Re e < 2000) (5) where Re e is the equivalent Reynolds number defined as: Re e = 2Md p 3μ f (1 ε). Fig. 3. Thermophysical properties of CO 2 at 8.5 MPa. Fig. 5. Friction factor for CO 2 at supercritical pressures in the heated sintered porous tube: (a) upward flow; (b) downward flow: p = MPa, T f,b = C, q w = to W/m 2, G = kg/h.

5 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) heating) in the sintered porous tube correspond very well with Eq. (5). However, as seen from Fig. 5, the friction factors for CO 2 at supercritical pressures flowing in the heated sintered porous tube are much higher than those predicted by Eq. (5) for both upward and downward flows. The increased friction factors may be due to the variable thermophysical properties and the acceleration of the fluid flow along the porous tube as the porous section is heated. The experimental results were used to develop two new correlations using the CO 2 thermophysical properties to predict the friction factors in a heated tube for upward and downward flows. f e = 48.1 Re (Upward flow) (7) e f e = 99.1 Re (Downward flow) (8) e The parameter Re e is defined as: ( ) n ( ) m Re e = Re ρw μw e (9) ρ f μ f Re e includes the effects of variable density and viscosity; ρ w and μ w are the average values of the density and viscosity based on the inside average wall temperatures and pressures; ρ f and μ f are the average values of the density and viscosity based on the average of the inlet and outlet temperatures and pressures. For upward flow: n = 3.85, m = 3.55 For downward flow: n = 3.47, m = 3.53 Eqs. (7) and (8) predict the friction factor much better than Eq. (5), as shown in Fig. 6. Because of the effect of buoyancy and variable thermophysical properties, the flow resistance for downward flow is larger than that for upward flow Convection heat transfer of supercritical pressure CO 2 in a porous tube Figs. 7 9 present the experimental results for the local heat transfer coefficients and the wall and fluid bulk temperatures for convection heat transfer of CO 2 at supercritical pressures in the vertical porous tube for upward and downward flows. In the Fig. 6. Correlations for the friction factor for CO 2 at supercritical pressures in heated sintered porous tube: (a) upward flow; (b) downward flow: p = MPa, T f,b = C, q w = to W/m 2, G = kg/h. Fig. 7. Local heat transfer coefficients and fluid and wall temperatures for different inlet temperatures in a porous tube, d = 4 mm, d p = mm, ε = 0.4, p 0 = 9.5 MPa, G = 1.0 kg/h, q w = W/m 2, solid symbols: upward flow, hollow symbols: downward flow.

6 344 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) Fig. 8. Local heat transfer coefficients and fluid and wall temperatures for different heat fluxes in a porous tube, d = 4 mm, d p = mm, ε = 0.4, p 0 = 9.5 MPa, G = 1.0 kg/h, T 0 =30 C, Re dp,0 = 83, solid symbols: upward flow, hollow symbols: downward flow. figures, the solid symbols are the data for upward flow, while the hollow symbols are the data for downward flow. The fluid bulk temperatures were calculated using the local pressure and the local enthalpy. Fig. 7 illustrates the local heat transfer coefficients and the wall and fluid bulk temperature distributions for different inlet fluid temperatures. The inlet temperature significantly influences the convection heat transfer for a given pressure, mass flow rate and heat flux due to the strong variations of the thermophysical properties of supercritical CO 2 with temperature for both upward and downward flows. The local heat transfer coefficients decrease with increasing inlet temperatures. For inlet fluid temperatures close to but higher than the pseudocritical temperature, T pc (T pc = 42.5 C for CO 2 at 9.5 MPa), the local heat transfer coefficients decrease continuously along the porous tube due to decreases of the thermophysical properties along the porous tube, especially the decrease of c p (see Fig. 3). However, for inlet fluid temperature much less than T pc, the local heat transfer coefficients do not decrease continuously along the porous tube, but reach a maximum for upward flow when the fluid bulk temperature is close to T pc. This phenomenon can be easily understood Fig. 9. Local heat transfer coefficients and fluid and wall temperatures for different pressures in a porous tube d = 4 mm, d p = mm, ε = 0.4, G = 1.0 kg/h, q w = W/m 2, T 0 =30 C, solid symbols: upward flow, hollow symbols: downward flow. from Fig. 3, which shows that c p varies sharply with temperature with a maximum at T pc. For downward flow, the local heat transfer coefficients along the porous tube first decrease, but then increase to a maximum when the fluid bulk temperature is very close to T pc, and then decrease continuously. The different distributions of the convection heat transfer coefficients for upward and downward flows are mainly due to the buoyancy. The increase in the local heat transfer coefficients near the exit can be attributed to thermal conduction in the wall. Fig. 8 illustrates the influence of heat flux on the local heat transfer coefficients and on the wall and fluid bulk temperatures along the porous tube. When the wall temperatures are much larger than T pc, the local heat transfer coefficients decrease continuously along the porous tube for both upward and downward flows. The main reason is that the thickness of the low thermal conductivity layer increases with increasing wall temperature along the porous tube, which suppresses the heat transfer from the wall. However, for T 0 < T pc and wall temperatures slightly higher than T pc, the local heat transfer coefficients reach a max-

7 P.-X. Jiang et al. / J. of Supercritical Fluids 38 (2006) imum for upward flow, but for downward flow along the porous tube the heat transfer coefficients first decrease as the flow develop but then increase and then decrease continuously when the fluid bulk temperatures are near T pc due to the influence of the specific heat which has a maximum at T pc. The influence of the heat flux on the local heat transfer coefficients is very complicated for T 0 < T pc. The heat transfer coefficients first increase with increasing heat flux to a maximum at a moderate heat flux and then decrease with increasing heat flux for both upward and downward flows. This phenomenon is caused by the strong variation of the thermophysical properties, especially the variation of c p. With increasing heat flux, the local CO 2 bulk temperatures and the local wall temperatures increase to and go above T pc. These very sharp variations of the fluid thermophysical properties include the maximum specific heat cause the local heat transfer coefficients to reach a maximum with increasing heat flux for T 0 < T pc. The different variations of the local heat transfer coefficients along the porous tube for upward and downward flows are mainly caused by the buoyancy. When the pressure is reduced to the critical pressure, the variations of the thermophysical properties are even greater with larger specific heats near T pc. Therefore, the convection heat transfer is more intensive. The effect of different pressures on the convection heat transfer in the porous tube is shown in Fig. 9. The local heat transfer coefficients increase with decreasing pressure (approaching p c ) for both upward and downward flows with the local heat transfer coefficients having maximums when the CO 2 bulk temperatures are near the pseudocritical temperature due to the sharp increase in the specific heat. At the same time, the effect of buoyancy increases with decreasing pressure. The variations of the local heat transfer coefficients with the fluid bulk temperature for different pressures at a mass flow rate of 1.0 kg/h are shown in Fig. 10. The trends for the variations of the local heat transfer coefficients are similar for the upward and downward flows with maximums near the pseudocritical temperature due to the sharp variations of the thermophysical properties, especially the variation of specific heat. 4. Conclusions The experimental results for the friction factors of CO 2 flowing in a sintered porous tube at supercritical pressures and constant temperature (without heating) correspond very well with the known correlation (Eq. (5)). However, the measured friction factors for CO 2 at supercritical pressures flowing in a heated sintered porous tube are much larger than those predicted by Eq. (5) for both upward and downward flows. Two new correlations are presented for upward and downward flows to predict the friction factors of supercritical CO 2 in heated porous tubes. The local heat transfer coefficients decrease with increasing inlet temperature when the wall temperatures are higher than the pseudocritical temperature T pc. When the inlet fluid temperature is higher than T pc, the local heat transfer coefficients decrease continuously along the porous tube. However, when the inlet fluid temperature is less than T pc, the local heat transfer coefficients reach a maximum when the fluid bulk temperature is near T pc. When the inlet temperature is below the pseudocritical temperature, the heat transfer coefficients reach a maximum with increasing heat flux on the wall. The local heat transfer coefficients increase when the pressure is close to the critical pressure. The variations of the local heat transfer coefficients with increasing fluid bulk temperatures have a maximum for both upward and downward flows near the pseudocritical temperature due to the sharp variations of the thermophysical properties, especially the specific heat. The buoyancy also influences the convection heat transfer in the porous media causing different variations of the local heat transfer coefficients along the porous tube for upward and downward flows. Acknowledgment Fig. 10. Comparison of local heat transfer coefficients for upward and downward flows: (a) p 0 = 9.5 MPa (b) p 0 = 8.5 MPa, d = 4 mm, d p = mm, ε = 0.4, G = 1.0 kg/h. The project was supported by the National Outstanding Youth Fund from the National Natural Science Foundation of China (no ).

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