The Journal of Supercritical Fluids

Transcription

1 J. f Supercritical Fluids 7 (212) ntents lists available at SciVerse ScienceDirect The Jurnal f Supercritical Fluids ju rn al h m epage: Flw and heat transfer characteristics f r22 and ethanl at supercritical pressures Pei-Xue Jiang a,, hen-ru Zha a,b, B Liu a a Beijing Key Labratry f O 2 Utilizatin and Reductin Technlgy/Key Labratry fr Thermal Science and Pwer Engineering f Ministry f Educatin, Department f Thermal Engineering, Tsinghua University, Beijing 184, hina b Institute f Nuclear and New Energy Technlgy, Tsinghua University, Beijing 184, hina a r t i c l e i n f Article histry: Received 21 December 211 Received in revised frm 2 June 212 Accepted 2 June 212 Keywrds: Supercritical pressures R22 Ethanl Frictinal pressure drp nvectin heat transfer a b s t r a c t This paper presents an experimental investigatin f the flw and cnvectin heat transfer characteristics f R22 and ethanl at supercritical pressures in a vertical small tube with an inner diameter f 1.4 mm. The heat flux ranges frm W m 2 t W m 2, the fluid inlet Reynlds number ranges frm t , and the pressure ranges frm 5.5 MPa t 1 MPa. The results shw that fr supercritical R22, the frictinal pressure drp increases significantly with the heat flux. At p = 5.5 MPa, Re in = 12, and a heat flux f 1 6 W m 2, the lcal heat transfer is greatly reduced due t the lw density fluid near the high temperature wall. Bth buyancy and flw acceleratin have little effect n the heat transfer. Fr supercritical ethanl, the frictinal pressure drp variatin with the heat flux is insignificant, while the lcal heat transfer cefficient increases as the enthalpy increases. Ethanl gives better flw and heat transfer perfrmance than R22 at supercritical pressures frm 7.3 MPa t 1 MPa fr heat fluxes f W m Elsevier B.V. All rights reserved. 1. Intrductin The third fluid cling technlgy is develped t prtect the high heat flux surface in cmbustin chamber in liquid rcket engines. In the third fluid cling system, the third fluid besides the xidizer and the fuel, which are referred as prpellant, is intrduced as the clant and circulated t cl the nzzle and cmbustr assembly. The third fluid is cntained in a clsed-lp cycle with the high temperature cmbustr wall as the heat surce and the lw temperature fuel as the cld sink [1]. The clant is circulated by a turbine-driven clant pump thrugh the passage frmed by a jacket enclsing the nzzle and cmbustr assembly with high heat flux frm the cmbustr absrbed by the clant, and then fed int the turbine t prduce wrk by expansin fr driving the xidizer pump, clant pump and fuel pump. Afterwards the clant vapr cndenses in a heat exchanger t heat the fuel r xidizer r bth; thereby returning the heat frm the cmbustr t the prpellant fed int the cmbustin chamber. In the third fluid cled liquid rcket engine, since the clant is circulated utside the chamber, the turbine utlet pressure is reduced and much higher turbine expansin ratis can be btained. Mrever, all f the prpellant is rrespnding authr. Tel.: ; fax: address: jiangpx@tsinghua.edu.cn (P.-X. Jiang). fed t the cmbustr which can perate at higher pressures; thus, the utput thrust is increased. During the heat absrbing prcess in the jacket enclsing the nzzle and cmbustr assembly, the clant (the third fluid) is usually abve its critical pressure, while during the heat rejectin prcess the clant (the third fluid) heats the prpellant at sub-critical pressures and cndenses. R22 and ethanl have been suggested as wrking fluids fr third fluid cling cycles in view f their thermphysical prperties, heat transfer and flw resistance prperties, critical parameters and safety. When the fluids are at supercritical pressures such as when absrbing heat frm the nzzle and cmbustr assembly, small fluid temperature and pressure variatins can result in drastic changes in the thermphysical prperties as shwn in Fig. 1 [2]. The specific heat, c p, reaches a peak at a certain temperature defined as the pseud critical temperature, T pc. Other prperties including the density, thermal cnductivity and viscsity als vary significantly within a small temperature range near T pc. The flw resistance and heat transfer are then expected t exhibit many special features due t the significant prperty variatins and the cnsequent buyancy and flw acceleratin effects [3]. In additin t the third fluid cling systems, flw and cnvectin heat transfer f supercritical fluids als ccur in many ther industrial applicatins including aerspace engineering, pwer engineering, chemical engineering, enhanced gethermal systems, O 2 strage and crygenic and refrigeratin engineering. Fr /$ see frnt matter 212 Elsevier B.V. All rights reserved.

2 76 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) Nmenclature B* nn-dimensinal buyancy parameter c p specific heat at cnstant pressure [kj kg 1 K 1 ] d tube diameter [m] g gravitatinal acceleratin [m s 2 ] G mass flux [kg m 2 s 1 ] Gr* Grashf number lcal heat transfer cefficient [W m 2 K 1 ] k turbulence kinetic energy [m 2 s 2 ] I heating current [A] ulk specific enthalpy [J kg 1 ] Kv nn-dimensinal flw acceleratin parameter p pressure [MPa] Pr Prandtl number Q heat quantity [W] q heat flux [W m 2 ] R inner radius f small tube [m] r distance frm the axis [m] Re Reynlds number T temperature [ ] u velcity [m s 1 ] x axial crdinate [m] Greek symbls p thermal expansin cefficient [K 1 ] ˇT isthermal cmpressin cefficient [Pa 1 ] ı tube wall thickness [m] thermal cnductivity [W m 1 K 1 ] mlecular viscsity [Pa s] fluid density [kg m 3 ] r electrical resistivity [ m] Subscripts ad adiabatic sectin f fluid i inner surface in inlet uter surface ut utlet pc pseud critical p induced by pressure variatin T induced by temperature variatin w wall instance, platelet transpiratin cling uses hydrgen r methane at supercritical pressures flwing thrugh chemically etched clant micrn scale channels in the platelet frmed by bnding tgether thin metal sheets t prtect high heat flux surfaces such as rcket thruster walls [4]. In pwer engineering applicatins, supercritical pressure water is widely used as the wrking fluid in thermal pwer statins. In the supercritical pressure water-cled reactr (SPWR), the supercritical pressure water absrbs fissin heat frm the fuel assembly in the reactr cre and enters the turbine at high temperature and high pressure, which enhances the thermal pwer cycle efficiency. Supercritical pressure water is als being actively cnsidered as the clant fr the breeder blanket in fusin pwer plants [5]. mprehensive researches n the in-tube flw and cnvectin heat transfer f supercritical fluids have been cnducted in the past several decades by Petukhv [3], Dmin [6], Prtppv [7], Plyakv [8], Shitsman [9], Burke et al. [1], Hall [11], Jacksn and Hall [12,13], Bringer and Smith [14], Schnurr [15], Tanaka et al. [16], Shiralkar and Griffith [17] fr applicatins f supercritical fluids in varius industrial fields. The wrking fluids have mstly been ρ/1, c p 5, μ/2 1 6, λ 1 3 ρ/5, c p 5, μ/2 1 6, λ λ μ 3 4 μ 6 ρ 9 T pc 12 T pc 15 T / 18 (a) R22 (p c =4.99 MPa, T =96.2º p = 7 MPa p =1 MPa 8 12 c p 16 ρ T / c ) λ 2 p = 7 MPa p =1 MPa T pc (b) Ethanl (p c =6.15 MPa, T =24.8º c ) c p 24 T pc 28 Fig. 1. Thermphysical prperty variatins with temperature water and carbn dixide. These results have prvided significant insight int the special features f the in-tube flw and cnvectin heat transfer f supercritical fluids. Several crrelatins have been develped fr the pressure drp and heat transfer cefficient f supercritical pressure fluids during heating based n the experimental and theretical results. Tarasva and Lent ev [18] measured the flw resistance f supercritical water flwing thrugh 3.34 mm and 8.3 mm smth vertical tubes during heating and fund that the measured results were lwer than the values f thse withut heating near the critical pint due t the viscsity decrease. Razumvskiy [19] claimed that the pressure drp resulting frm the density variatin culd nt be ignred fr large ratis f the heat flux t the mass flux based n their studies f supercritical water flwing thrugh a 6.28 mm smth vertical tube during heating. Fr the heat transfer, Shitsman [9] fund that, fr relatively large tubes (d in = 8 mm fr example), the lcal wall temperatures varied nn-linearly and lcal heat transfer deteriratin was bserved in buyancy-aided flw cases (upward flw in a heated passage) resulting frm the buyancy effect whereas in buyancy-ppsed flw cases (dwnward flw in a heated passage) the lcal wall temperature varied smthly. Jacksn and Hall [12] explained the in-tube buyancy affected cnvectin heat transfer behavir fr supercritical fluids using a semi-empirical thery and prpsed a

3 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) Fig. 2. Schematic f experimental system. nn-dimensinal buyancy parameter, B*, t evaluate the significance f the buyancy effect [13]. This semi-empirical thery had agreed fairly well with mst f the buyancy affected experimental results in the literature [2]. When the tube size is reduced and the heat flux is increased further, flw acceleratin is expected t ccur due t the extreme axial temperature and pressure variatins. Jacksn [5] discussed the effects f the heat flux n frced cnvectin heat transfer f fluids at supercritical pressures. With the fluid temperature increases r the pressure decreases alng the tube, the density decreases and the fluid accelerates, which reduces the turbulence prductin and the heat transfer. When the heat flux is lw, the effect is small, but at very high heat fluxes, the turbulence culd be significantly reduced and the flw may even re-laminarise. This effect dminates in high heat flux flws and results in verall heat transfer deteriratin. McEligt et al. [21] prpsed the nn-dimensinal heating acceleratin parameter, Kv, t assess the flw acceleratin effect due t thermal expansin. Kurganv et al. [22] pinted ut that unlike the buyancy effect, the flw acceleratin effect is imprtant nly in small diameter tubes. Fr large diameter tubes the buyancy effect is the main factr, fr mderate diameter tubes the flw acceleratin effect can als be ignred if the buyancy effect can be ignred, while fr small diameter tubes, the flw acceleratin effect can be very imprtant. Li et al. [23] investigated the cnvectin heat transfer f O 2 at supercritical pressures in a 2 mm diameter vertical small tube and shwed that fr Re in = 9 1 3, when the heat flux was higher than W m 2, lcal heat transfer deteriratin was bserved in the upward flws, whereas n such behavir appeared in the dwnward flws, which indicated that the buyancy effect strngly influenced the heat transfer. The flw acceleratin due t heating was insignificant. Jiang et al. [24,25] studied the heat transfer f supercritical O 2 in a.27 mm diameter vertical mini tube and shwed that when the inlet Reynlds numbers exceeded 4 1 3, the buyancy and flw acceleratin had little influence n the lcal wall temperature, with n heat transfer reductin bserved in either flw directin. Hwever fr relatively lw Reynlds numbers (< ) and high heat fluxes ( W m 2 fr example), the lcal wall temperatures varied nn-linearly alng the tube in bth upward and dwnward flws, with the cnvectin heat transfer cefficients in dwnward flws higher than thse in upward flws. The experimental results indicated that fr.27 mm tubes, the flw acceleratin due t heating strngly influenced the turbulence and reduced the heat transfer fr high heat fluxes. The buyancy effect still culd nt be neglected althugh relatively small even with strng heating. Fr supercritical fluids flwing thrugh 1 mm channels at heat fluxes up t 1 6 W m 2, such as when R22 r ethanl are used t cl the high heat flux surface in the liquid rcket engine cmbustin chamber, the radial and axial temperature gradients are extremely large. The flw and heat transfer are expected t be mre significantly affected by the severe temperature variatins, with strng buyancy and flw acceleratin effect pssibly be induced by the radial and axial density variatins. This paper presents an experimental investigatin f the flw and cnvectin heat transfer f R22 and ethanl at supercritical pressures in a vertical tube with an inner diameter f 1.4 mm fr varius pressures, heat fluxes, and mass fluxes. The effects f the thermphysical prperty variatins, buyancy and flw acceleratin are evaluated and discussed. The flw and heat transfer characteristics f R22 and ethanl are cmpared. The results are helpful t btaining a better understanding f the heat transfer characteristics f supercritical fluids in small tubes at high heat fluxes with large temperature differences between the fluid and the wall. The results are als f great help when develping empirical crrelatins fr the flw and heat transfer with severe radial thermphysical prperty variatins in the cling passage fr designing and ptimizing the third fluid cling systems. 2. Experimental system and data reductin 2.1. Experimental apparatus The experimental system is illustrated in Fig. 2. The wrking fluid (R22 r ethanl) flws frm the cntainer t an accumulatr and then thrugh a filter befre it is pressurized by the supercritical fluid pump (Thar P-35) and heated in the pre-heater t the required inlet temperature. A manstat is installed after

4 78 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) Data reductin methd Frictinal pressure drp The pressure drp measured in the experiments, p, includes the pressure drp in the inlet and utlet adiabatic sectins, p ad,in and p ad,ut, the frictinal pressure drp in the heating sectin, p f, and the pressure drp resulting frm the fluid expansin alng the test sectin during heating, p a [26]. p = p f + p ad,in + p ad,ut + p a (2) The pressure drps in the inlet and utlet adiabatic sectins are calculated as: G 2 L p ad,in = f in,in 2 in d G 2 L ut p ut = f,ut 2 ut d (3) Fig. 3. SEM phtgraph f the test sectin. the pump t stabilize the system pressure and mass flw rate. The mass flw rate is measured by the mass flwmeter (Mdel MASS21/MASS6, MASSFLO, Danfss). The fluid is heated in the test sectin by Jule heating frm a current stabilized pwer surce, and cled by the sub-cler after leaving the test sectin. A decmpressin valve is installed t adjust and stabilize the system pressures. Then the fluid flws back t the supercritical pump. The pump head f the supercritical pump is cled by a cling bath. The test sectin is a vertical smth stainless steel 1r18Ni9Ti tube. The length f the heating sectin is 152 mm, and the length f the adiabatic sectin befre and after the heating sectin is bth 52 mm. An SEM phtgraph f the tube crss sectin is shwn in Fig. 3. The test sectin is cnnected t the test lp by flanges and high-pressure fittings. The inner tube diameter is 1.4 mm and the uter diameter is 2.11 mm. The test sectin is insulated thermally and electrically frm the test lp by a layer f plytetrafluethylene (PTFE) placed between the flanges and between the screws and the flanges. The flw directin (upward r dwnward) f the fluid flwing thrugh the test sectin is switched by a set f valves. Mixers are installed befre the pints where the inlet and utlet fluid temperatures are measured by accurate RTDs (Pt). The inlet pressure is measured by a pressure transducer (EJA43A) and the pressure drp between the inlet and utlet is measured by a differential pressure transducer (Mdel EJA13A). The lcal uter wall temperatures f the heating sectin are measured using 15 equally spaced K-type thermcuples welded nt the uter tube surface. The lcal heat flux is calculated frm the heating current and the electrical resistance f the tube. The electrical resistivity variatin with temperature is experimentally measured. The test sectin is first evacuated by vacuum-pumping, and then heated by a cnstant current until the wall temperature and the heating vltage acrss the test sectin are steady. Then the electrical resistance,, at the measured wall temperature is calculated as: = (U/I) ((d 2 d 2 i )/4) L The system is assumed t be steady when the wall temperature and the inlet and utlet fluid temperature variatins are all within ±.2 and the flw rate and inlet pressure variatins are within ±.2% fr at least 1 min. A crrelatin is then established t crrelate the electrical resistivity t temperatures fr temperatures f 2 3. (1) where L in and L ut are the lengths f the adiabatic inlet and utlet sectins, in and ut are the densities based n the inlet and utlet bulk temperatures, G is the mass flux, and the frictin factrs fr the inlet and utlet adiabatic sectins, f,in and f,ut, are calculated using Finlenk equatin [27]: f,in = (1.82lg Re in 1.64) 2 f,ut = (1.82lg Re ut 1.64) 2 (4) where Re in and Re ut are based n the fluid inlet and utlet average velcities and prperties respectively. The inlet and utlet average velcities are calculated frm the mass flux and the lcal densities; the lcal prperties are determined by the lcal bulk temperatures. The pressure drp resulting frm the fluid expansin alng the test sectin during heating is calculated as [26]: ( 1 p a = G 2 1 ) (5) ut in Thus, the frictinal pressure drp thrugh the heating sectin is calculated as: p f = p p ad,in p ad,ut p a (6) Heat transfer cefficient The lcal heat transfer cefficient,, at each axial lcatin is calculated as (x) = (7) T w,i (x) T f (x) The lcal heat flux n the inner surface, (x), is calculated as: (x) = I2 R x (t) Q lss,x d i x = I2 (t)x/ [ (d 2 d 2 i )/4] Q lss,x d i x (8) The test sectin heat lss, Q lss, x, is determined frm the temperature difference between the tube wall and the surrundings by a crrelatin, which is btained by plynmial fitting the experimentally measured heat lss (which is assumed t be equal t the electrical pwer input t the tube when evacuated by vacuumpumping) and the temperature difference between the tube wall and the surrundings. The lcal bulk fluid temperature, T f (x), is btained using the NIST sftware REFPROP 8. [2] and the lcal bulk fluid enthalpy, (x), calculated as: (x) =,in + (x)d i x (9) G

5 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) The Reynlds number based n the mean bulk temperature is defined as: Re = ud i (1) The inner wall temperature, T w,i (x), is calculated using the measured uter wall temperature, T w, (x), and the internal heat surce, q v, as: T w,i (x) = T w, (x) + q v(x) [ ] d 2 16 d 2 q v (x) i + 8 d2 ln d i (11) d where q v is calculated as: q v (x) = I2 R x (t) Q s,x [(d 2 d 2)/4] x i 2.3. Experimental uncertainty analysis (12) The experimental uncertainty in the lcal heat transfer cefficient mainly results frm the heat flux and the temperature measurement uncertainties. The thermcuples and the RTDs are calibrated by the Natinal Institute f Metrlgy, PR hina befre installatin. The accuracy f the RTDs used t measure the inlet and utlet bulk temperatures is ±.1 ; the maximum uncertainty f the K-type thermcuples used t measure the uter wall temperature is ±1.2 within the temperature range used in the present study. The average temperature difference between the wall and the fluid is greater than 1. The uncertainty f the temperature difference is evaluated t be 12.1%. The verall uncertainty f the heat flux is mainly related t the accuracy f the heat input t the fluid, which is determined by the heating electric current and the vltage, the heating area, and the heat lss. The accuracy f the heating electric current and vltage are 1.1% and.28% respectively; the accuracy f the heating area is.3%, which is mainly determined by the heating sectin length measured by vernier caliper with accuracy f ±.2 mm (the tube diameter is measured by SEM, and the uncertainty is negligible) and the uncertainty induced when welding the heating electrdes, which is abut ±.5 mm; the heat lss is less than 4%, which is assumed t be the heat lss uncertainty. Therefre, the verall uncertainty f the heat flux is estimated t be 4.2%. The verall uncertainty f the heat transfer cefficient 12.8% is then calculated frm the uncertainty f the temperature difference, 12.1%, and the heat flux, 4.2%. The pressure transducer (Mdel EJA43A) accuracy is.75% f the full range f 25 MPa, thus, the measurement uncertainty is 18.8 kpa. The minimum inlet pressure in the present cases is 5.5 MPa, therefre, the uncertainty in the inlet pressure is estimated t be.3%. The accuracy f the differential pressure transducer (Mdel EJA13A) is.75% f the full range f 125 kpa, thus, the measurement uncertainty is.94 kpa. The minimum pressure drp in the present cases is 5 kpa, therefre, the uncertainty in the pressure drp is estimated t be 1.9%. Accrding t the instructin f the mass flwmeter, the mass flw rate uncertainty is.1% within 5 1% f the mass flwmeter full range f 25 kg h 1, which is kg h 1. Since the mass flw rate ranges frm 5.5 kg h 1 t 11.7 kg h 1, the mass flw rate uncertainty is estimated t be.1% in the present cases. The uncertainty f the frictinal factr calculated frm the frictinal pressure drp mainly results frm the uncertainties f the measured pressure drp, the mass flw rate and the heating sectin length, which are 1.9%,.1% and.3% respectively. Therefre, the uncertainty f the frictinal factr is 1.9%. Table 1 Test cnditins. Wrking fluids R22, ethanl Inner tube diameter (mm) 1.4 Inlet pressures (MPa) Heat fluxes (W m 2 ) Fluid temperatures ( ) 25 2 Fluid inlet Reynlds numbers Experimental results and discussin The frictinal pressure drp and the cnvectin heat transfer characteristics f the supercritical pressure R22 and ethanl flwing thrugh a 1.4 mm inner diameter vertical tube are experimentally investigated fr the cnditins summarized in Table 1. The frictinal pressure drp thrugh the test sectin, the lcal wall temperature, the lcal heat transfer cefficient, the buyancy parameter B*, the flw acceleratin parameter, Kv, and its tw cmpnents, Kv T and Kv p, are evaluated fr varius inlet Reynlds numbers, pressures and wall heat fluxes t examine the effects f thermphysical prperty variatins, buyancy and flw acceleratin due t thermal expansin and pressure drp n the heat transfer Frictinal pressure drp The influence f prperty variatins, especially the effect f density and viscsity variatins with the temperature n the frictinal pressure drp is evaluated by cmparing the frictinal pressure drps thrugh the heat sectin fr varius heat fluxes in Fig. 4 with thse predicted using Filnenk equatin [27], which is based n cnstant prperty flw data and neglects density and viscsity variatins with temperature. The frictin factr, f, is calculated as f = (1.82lg Re 1.64) 2 (13) where Re is based n the average f the inlet and utlet fluid temperature. The predicted frictinal pressure drps using Petukhv crrelatin [3] and Itaya crrelatin accunting fr the influence f viscsity [28] based n the wall temperature are als presented in Fig. 4. Petukhv crrelatin includes a viscsity crrectin term, ( b / w ), t crrect the influence f the fluid viscsity near the wall, / kw m Fig. 4. Frictinal pressure drps fr varius heat fluxes. R22, p = 5.5 MPa, G = 4 kg m 2 s 1, upward flw. Slid dt: measured results; slid line: predictins by Filnenk equatin. Dash line: predictins by Petukhv crrelatin; dt line: predictins by Itaya crrelatin.

6 8 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) / kw m / kw m Fig. 5. Frictinal pressure drps fr varius heat fluxes. R22, p = 5.5 MPa, G = 2 kg m 2 s 1, upward flw. Slid dt: measured results; slid line: predictins by Filnenk equatin. Dash line: predictins by Petukhv crrelatin; dt line: predictins by Itaya crrelatin. Fig. 6. Frictinal pressure drps fr varius heat fluxes. R22, p = 7.3 MPa, G = 2 kg m 2 s 1, upward flw. Slid dt: measured results; slid line: predictins by Filnenk equatin. Dash line: predictins by Petukhv crrelatin; dt line: predictins by Itaya crrelatin. and the frictinal factr with the prperty variatin crrectin, f vp, is then: f vp = 1 ( 7 ) b (14) f 6 w where f is calculated using Eq. (13). In Itaya crrelatin f vp is calculated as: ( f vp w ).72 = (15) f b where,.314 f = lg Re b + (lg Re b ) 2 (16) Since the heat flux is relatively high in the present study, the lcal fluid temperature varies significantly alng the tube and the lcal frictinal resistance is significantly affected by the lcal prperties; thus, the lcal frictinal pressure drps in each subsectin are calculated as: x G 2 p f,x = f vp,x (17) d 2 b,x where f vp is the lcal frictinal factr calculated using the crrelatins, x is the length f each subsectin and the thermphysical prperties are based n the lcal wall and fluid temperatures in each subsectin. The predicted frictinal pressure drp alng the entire heating sectin, p f, is then btained by summing up the lcal pressure drps in each subsectin. The measured and predicted frictinal pressure drps f R22 fr varius heat fluxes at p = 5.5 MPa fr upward flw are shwn in Fig. 4 fr G = 4 kg m 2 s 1 and in Fig. 5 fr G = 2 kg m 2 s 1. p f increases with increasing heat flux, and increases significantly when the heat flux exceeds a certain value. This is mainly due t that the fluid temperature increases with increasing heat flux, s the fluid density decreases and the velcity increases t maintain flw cntinuity. The frictinal pressure drp then increases as a result. When the fluid temperature appraches T pc, the density decreases and the velcity severely increases, the frictinal pressure drp sharply increases. Althugh the fluid viscsity decreases as the temperature increases, which reduces the frictin between the fluid and the wall t sme extent, the effect f density decreasing verwhelms the viscsity decrease which results in increasing frictinal pressure drp as shwn in Figs. 4 and 5. Fr relatively lw heat fluxes, such as = 341 kw m 2 in Fig. 4 and = 136 kw m 2 in Fig. 5, the temperature difference between the fluid and the wall is small, and the prperty variatins are insignificant in the tube. Filnenk equatin predicts the measured frictinal pressure drp fairly well. In additin, there is n significant difference amng the Petkhv crrelatin predictins, Itaya crrelatin predictins and the measured results. As the heat flux increases, bth the fluid temperature and the wall temperature rise, and the temperature difference between the fluid and the wall increases resulting in sharp prperty variatins acrss the tube and a remarkable effect f the fluid layer near the wall (the temperature f which is similar t the wall temperature) n the frictinal resistance. Since in the present cases, the wall temperature is much higher than the fluid temperature in the center (which is clse t the bulk temperature), the fluid density near the wall decreases, which increases the fluid velcity near the wall mre than in the center and intensifies the fluid mixing near the wall; thus, the frictin between the fluid and the wall increases as a result. The fluid viscsity decreases near the wall, which reduces the frictin between the fluid and the wall t sme extent. The effect f neither the density nr viscsity variatins near the wall n the frictinal pressure drp can be neglected since the tradeff between the density and viscsity variatins determines the frictinal pressure drp. Fr = 551 kw m 2 in Fig. 4 and = 242 kw m 2 and 327 kw m 2 in Fig. 5, the tw effects almst balance; thus, Petukhv and Itaya crrelatins which nly cnsider the viscsity variatin effect underestimate the frictinal pressure drp. Filnenk equatin, which evaluates the prperties based nly n the bulk temperature, prduces better results. As the heat flux increases further, the bulk temperature appraches T pc and the wall temperature exceeds T pc, s the fluid density near the wall decreases and the fluid stays in a gas-like state. The flw resistance increases drastically, which verwhelms the viscsity decrease; thus, Filnenk equatin underpredicts the frictinal pressure drp and the ther tw crrelatins prduce much lwer results as shwn in Figs. 4 and 5. When bth the bulk and wall temperatures exceed T pc fr higher heat fluxes, = 125 kw m 2 and 1335 kw m 2 in Fig. 4 and = 728 kw m 2 and 777 kw m 2 in Fig. 5, the density and viscsity variatins effects n the flw resistance decrease; thus, the predictins f all three crrelatins apprach the measured results.

7 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) MPa 1 MPa / kw m / kw. m Fig. 7. Frictinal pressure drps fr varius heat fluxes. Ethanl, p = 1 MPa, G = 4 kg m 2 s 1, upward flw. Slid dt: measured results; slid line: predictins by Filnenk equatin. Dash line: predictins by Petukhv crrelatin; dt line: predictins by Itaya crrelatin MPa 1 MPa (a) R22 Fig. 6 presents the measured and predicted frictinal pressure drps f R22 fr varius heat fluxes at p = 7.3 MPa, G = 2 kg m 2 s 1, and upward flw. As in Figs. 4 and 5, the predicted values using Filnenk equatin withut the prperty variatin crrectin terms based n the wall temperature agree fairly well with the measured results fr relatively lw heat fluxes, while the ther crrelatins with nly viscsity crrectin terms underpredict p f. As the heat fluxes increase, the thermphysical prperties differences between the fluid center and the wall increase, s the predicted values deviate frm the measured results. The ethanl density and viscsity variatins differ frm thse f R22, which prduces different results when cmparing the measured and predicted p f, as shwn in Fig. 7. The frictinal pressure drp variatins with the heat flux fr ethanl are relatively insignificant. The ethanl density variatin with temperature is less severe than that f R22 fr the temperature range in the present study (since the critical temperature fr ethanl, 248, is relatively high, the fluid and wall temperatures are belw T pc in mst cases), while the viscsity decreases drastically with the temperature; thus, the flw resistance reductin due t the viscsity decrease verwhelms the density variatin effect fr ethanl. Even fr lw heat fluxes, the fluid viscsity near the wall based n the wall temperature, is much smaller than that based n the bulk temperature, which reduces the flw resistance. Thus, the measured frictinal pressure drps are generally lwer than the predictins f Filnenk equatin using prperties based n the bulk temperature. Itaya crrelatin with the viscsity crrectin based n the wall temperature prduces better results than the ther tw crrelatins as shwn in Fig. 7. The influences f pressure n the frictinal pressure drps f R22 and ethanl are shwn in Fig. 8(a) and (b). Fr p = 7.3 MPa, which is clse t the critical pressure, p c = 4.99 MPa, the frictinal pressure drp varies mre significantly with the heat flux mainly due t the thermphysical prperty variatins, especially the sharp density decrease with temperature as the pressure appraches p c. Hwever, fr p = 1 MPa, the thermphysical prperty variatins are relatively small; thus, the increase in the frictinal pressure drp with the heat flux is smaller. As the pressure increases t 1 MPa, the frictinal pressure drp decreases by 2 3% as shwn in Fig. 8(a) and (b). The frictinal pressure drps fr R22 and ethanl are cmpared fr p = 7.3 MPa and 1 MPa in Fig. 9(a) and (b). The flw resistance is clsely related t the thermphysical prperties f the fluid near the wall evaluated at the wall temperatures, especially fr the cases / kw. m -2 (b) Ethanl Fig. 8. Frictinal pressure drps fr varius pressures. G = 4 kg m 2 s 1, upward flw with relatively large heat fluxes where the wall temperature is high and the temperature difference between the bulk fluid and the wall is quite large (greater than 2 in mst cases). The R22 density variatin is sharper than the ethanl density variatin while the ethanl viscsity variatin is sharper than the R22 viscsity variatin, as shwn in Fig. 1(a) and (b). Fr R22, the flw resistance increases resulting frm the large density decrease, while fr ethanl, the viscsity decreasing with the temperature significantly reduces the flw resistance and the frictinal pressure drp fr ethanl is smaller than fr R22 when the pressure and the mass flux are the same. Fr p = 1 MPa, the ethanl frictinal pressure drp is 1 2% lwer than fr R22, and fr p = 7.3 MPa, where the prperty variatins are mre significant, the ethanl frictinal pressure drp is 2 3% lwer than fr R Heat transfer Heat transfer f R22 The lcal wall temperature and heat transfer cefficient variatins with the lcal enthalpy are shwn in Fig. 11(a) and (b) fr varius heat fluxes at p = 5.5 MPa, G = 2 kg m 2 s 1 and upward flw. The lcal wall temperature increases with the enthalpy when the heat flux is relatively lw, = 136 kw m 2, 242 kw m 2 and 327 kw m 2. As the bulk temperature increases and appraches T pc, the specific heat, c p, increases greatly, which enhances the

8 82 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) R22 Ethanl 12 R22 Ethanl 4 ρ/ kg. m R22 Ethanl 9 / kw. m -2 (a) p=7.3 MPa μ 1 6 / Pa. s T/ (a) Density R22 Ethanl / kw. m T/ (b) Viscsity (b) p=1 MPa Fig. 1. Density and viscsity variatins fr R22 and ethanl at p = 1 MPa. Fig. 9. Frictinal pressure drps fr R22 and ethanl. G = 4 kg m 2 s 1, upward flw. heat transfer between the fluid and the wall, and the heat transfer cefficient increases as a result, as shwn in Fig. 11(b). As the heat flux increases t = 521 kw m 2 and 631 kw m 2, the fluid temperatures pass thrugh T pc, the wall temperatures are abve T pc and the lcal enthalpy increases alng the test sectin. The lcal wall temperature firstly increases t a lcal maximum, then decreases, and increases again. This creates minimum lcal heat transfer cefficient where the maximum wall temperature ccurs. The heat transfer cefficient then increases when the bulk temperature passes thrugh T pc and then decreases. This is mainly due t that as the bulk temperature appraches T pc, the bulk specific heat increases greatly, which enhances the heat transfer as a result. Hwever, when the heat flux is relatively high, the wall temperatures are usually fairly high as well, s the fluid density, thermal cnductivity and specific heat near the wall are quite lw, which impairs the heat transfer between the fluid and the wall, and the heat transfer cefficient decreases. As the fluid temperature increases and appraches T pc, the bulk averaged specific heat acrss the tube increases, which vercmes the negative effect f the lw density, lw thermal cnductivity and lw specific heat near the wall; thus, the heat transfer recvers, the wall temperature decreases and the heat transfer cefficient increases. As the fluid and wall temperatures increase t much higher than T pc, the fluid density, thermal cnductivity and specific heat decrease s the heat transfer is reduced and the heat transfer cefficient decreases again as shwn in Fig. 11(b). When the heat flux increases further t 728 kw m 2 and 777 kw m 2, the lcal wall temperature increases dramatically t a maximum and then decreases, with a much sharper peak bserved. The temperature difference between the fluid and the wall can be as high as hundreds f degrees at the peak, as shwn in Fig. 11(a), the density, thermal cnductivity and specific heat near the wall are much lwer, which significantly reduces the heat transfer. As the bulk fluid temperature appraches T pc, the heat transfer recvers due t the increased bulk specific heat. The lcal wall temperature decreases and the lcal heat transfer cefficient increases. As the fluid temperature increases further t far abve T pc, the fluid stays in a gas-like state and the heat transfer between the fluid and the wall is again reduced s the lcal wall temperature increases as shwn in Fig. 11(a). The lcal temperature and heat transfer cefficient variatins with the lcal enthalpy fr varius heat fluxes fr R22 with G = 4 kg m 2 s 1 are shwn in Fig. 12(a) and (b). Fr heat fluxes f kw m 2, the lcal wall temperature increases with the enthalpy. When the fluid temperature is less than T pc, and the wall temperature is less than r near T pc, the heat transfer cefficient variatin with the enthalpy is relatively small. As the fluid and wall temperature increase, the wall temperature is much higher than T pc, s the density, thermal cnductivity and specific heat f the high temperature fluid near the wall are very lw, which reduces the heat transfer. The heat transfer cefficient between

9 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m -2 T w, T f / T w, T f / (a) Temperature (a) Temperature kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m (b) Heat transfer cefficient Fig. 11. Lcal wall temperatures and heat transfer cefficients fr varius heat fluxes. R22, p = 5.5 MPa, G = 2 kg m 2 s 1, upward flw. Symbls in (a): wall temperature; slid line: fluid temperature; dash dt line: pseud critical temperature (b) Heat transfer cefficient Fig. 12. Lcal wall temperatures and heat transfer cefficients fr varius heat fluxes. R22, p = 5.5 MPa, G = 4 kg m 2 s 1, upward flw. Symbls in (a): wall temperature; slid line: fluid temperature; dash dt line: pseud critical temperature the fluid and the wall is further reduced as the heat flux and wall temperature increase as shwn in Fig. 12(b). When the heat flux increases t kw m 2, a lcal maximum wall temperature is bserved with higher maximums at higher heat flux, as shwn in Fig. 12(a), but nt as high as in the cases in Fig. 11(a). The lcal heat transfer deteriratin resulting frm the lw density fluid layer near the wall is reduced with increasing mass flux as shwn by cmparing the lcal wall temperature variatins in Figs. 11 and 12. When the pressure increases t 1 MPa, the thermphysical prperty variatins with temperature are smaller than fr p = 5.5 MPa, s the heat transfer characteristics are quite different as shwn in Fig. 13(a) and (b), which present the lcal wall temperature and heat transfer cefficient variatins with the enthalpy fr p = 1 MPa, G = 4 kg m 2 s 1, and upward flw. The lcal wall temperature increases with the enthalpy withut a lcal maximum and with n increase in the cefficient dwnstream fr the heat fluxes used in the present study. The lcal heat transfer cefficient decreases with the enthalpy as shwn in Fig. 13(b) mainly due t the increase at the lcal wall temperature and the wall t fluid temperature difference. The temperature difference increases further when the heat flux increases since the high temperature fluid near the wall has a lw density, lw thermal cnductivity and lw specific heat which causes the lcal heat transfer cefficient t decrease as the enthalpy increases. The heat transfer cefficients at varius pressures fr R22 are cmpared in Fig. 14. When the pressure is far abve p c, which is 4.99 MPa fr R22, such as p = 7.3 MPa and 1 MPa, the heat transfer cefficient is relatively lw and the variatin with the enthalpy is relatively small. As the pressure appraches p c, 5.5 MPa fr example, the heat transfer cefficients are 1 2% higher thse at 7.3 MPa and 1 MPa at the same enthalpy as shwn in Fig Heat transfer f ethanl The lcal wall temperature and heat transfer cefficient variatins with the lcal enthalpy fr varius heat fluxes at p = 7.3 MPa, G = 4 kg m 2 s 1 and upward flw fr ethanl are shwn in Fig. 15(a) and (b). The lcal wall temperature variatin is small while the enthalpy is small. Hwever, as the enthalpy becmes relatively large near the test sectin utlet, the wall temperature increases significantly and the heat transfer cefficient first increases and then decreases. Fr ethanl, the viscsity decreases sharply with temperatures as shwn in Fig. 1(b); thus, as the temperature and the enthalpy increase, the viscsity decreases which intensifies the fluid turbulence, especially fr fluid near the wall which is mst influenced by the high wall temperature. The

10 84 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m -2 T w, T f / kw. m kw. m -2 T w, T / f (a) Temperature kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m -2 (b) Heat transfer cefficient Fig. 13. Lcal wall temperatures and heat transfer cefficients fr varius heat fluxes. R22, p = 1 MPa, G = 4 kg m 2 s 1, upward flw. Symbls in (a): wall temperature; slid line: fluid temperature; dash dt line: pseud critical temperature (a) Temperature kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m (b) Heat transfer cefficient Fig. 15. Lcal wall temperatures and heat transfer cefficients fr varius heat fluxes. Ethanl, p = 7.3 MPa, G = 4 kg m 2 s 1, upward flw. Symbls in (a): wall temperature; slid line: fluid temperature; dash dt line: pseud critical temperature Fig. 14. Heat transfer cefficients fr varius pressures. R22, G = 4 kg m 2 s 1, upward flw. Slid: 1 MPa; hllw: 7.3 MPa; center-crssed: 5.5 MPa viscsity decreases significantly and the turbulence is intensified as a result; therefre, the heat transfer between the fluid and the wall is further enhanced. mpared with R22, the ethanl density variatin with temperature is relatively small, as shwn in Fig. 1(a), s the negative effect f the density decrease f the high temperature fluid near the wall n the heat transfer is verwhelmed by the psitive effect f the viscsity decrease, which then prmpts an increase in the heat transfer cefficient with the enthalpy. Hwever, as the fluid temperature and the enthalpy increase further near the utlet, the fluid density, especially the fluid density near the wall decreases; thus, the wall temperature increases and the heat transfer cefficient decreases. Similar variatins are bserved fr the lcal wall temperature and heat transfer cefficient variatins with the enthalpy fr varius heat fluxes at p = 1 MPa, G = 4 kg m 2 s 1 and upward flw in Fig. 16(a) and (b). The heat transfer cefficients at p = 7.3 MPa and 1 MPa fr ethanl are cmpared in Fig. 17. Except fr the data affected by the high temperature fluid near the wall near the utlet, the heat transfer cefficient generally increases with the enthalpy fr bth p = 7.3 MPa and 1 MPa. The pressure effect n the heat transfer cefficient is quite small with the heat transfer cefficients fr 7.3 MPa nly slightly higher that thse fr 1 MPa since the frmer is clser t the critical pressure fr ethanl, 6.15 MPa.

11 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m T w, T / f kw. m (a) Temperature kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m -2 (b) Heat transfer cefficient Fig. 16. Lcal wall temperatures and heat transfer cefficients fr varius heat fluxes. Ethanl, p = 1. MPa, G = 4 kg m 2 s 1, upward flw. Symbls in (a): wall temperature; slid line: fluid temperature; dash dt line: pseud critical temperature T f / Fig. 18. Heat transfer cefficients fr R22 and ethanl. p = 1. MPa, G = 4 kg m 2 s 1, upward flw. Slid: R22 (T pc = fr 1 MPa); hllw: ethanl (T pc = fr 1 MPa) mparisn f R22 and ethanl heat transfer cefficients at supercritical pressures The heat transfer characteristics f R22 and ethanl at supercritical pressures differ due t their thermphysical prperty variatins in these perating cnditins. The heat transfer cefficient variatins with bulk fluid temperature, T f, are cmpared in Fig. 18. The heat transfer cefficients fr R22 decrease with the T f whereas thse fr ethanl increase with T f. The higher T f is, the larger the differences between the heat transfer cefficients fr ethanl and thse fr R22 are. Generally, the heat transfer cefficients fr ethanl are 5% t even several times higher than thse fr R22 fr similar fluid temperature, pressures and mass fluxes. This is related t the thermphysical prperty characteristics, especially the viscsity and density variatins with temperature fr R22 and ethanl. Fr relatively higher heat fluxes as in the present study, the wall temperature is quite high and the temperature difference between the fluid and the wall is large, s the radial prperty variatins in the tube are usually significant and the influence f the thermphysical prperties evaluated at the wall temperature n the heat transfer cefficients is expected t be mre significant than the effect at the bulk prperties Fig. 17. Heat transfer cefficients fr varius pressures. Ethanl, G = 4 kg m 2 s 1, upward flw. Slid: 1 MPa; hllw: 7.3 MPa Influence f the buyancy During the supercritical heat transfer in a tube, the fluid thermphysical prperties change drastically when the temperatures are near the pseud critical temperature. These strng fluid prperty variatins in bth the radial directin (frm the fluid cre t the wall) and the axial directin are expected t affect the heat transfer when the flw passes thrugh the near critical regin. A density gradient is induced acrss the tube by the radial temperature gradient between the fluid cre and the wall. With the relatively high heat fluxes used in the present study, which are kw m 2, the temperature difference between the bulk fluid and the wall can be as high as 2. The radial density gradient resulting frm such large temperature differences are quite sharp, with the high temperature fluid adjacent t the wall in a highly gas-like state with a fairly lw density while the fluid in the cre is still in a liquid-like state. Therefre, the high temperature fluid adjacent t the wall tends t flw upwards due t buyancy. Fr upward flw cases, the upwards buyancy frce near the wall is in the flw directin and accelerates the flw near the wall mre than in the cre, s the average velcity difference between the wall regin and the cre regin is reduced. The shear stresses between the wall and the cre and the turbulence prductin are reduced, and the heat transfer is reduced as a result. Fr dwnward

12 86 P.-X. Jiang et al. / J. f Supercritical Fluids 7 (212) kw. m kw. m kw. m kw. m kw. m kw. m -2 1E-6 1E kw. m kw. m kw. m kw. m kw. m kw. m T w, T / f B* 1E-8 1E-9 1E (a) G=2 kg m -2 s T / f Fig. 19. Lcal wall temperatures fr upward and dwnward flws. R22, p = 5.5 MPa, G = 2 kg m 2 s 1. Symbls: wall temperature (slid: upwards; hllw: dwnwards). Slid line: fluid temperature; dash dt line: pseud critical temperature fr 5.5 MPa. flw cases, the buyancy frce near the wall is ppsite t the flw directin; thus, the velcity gradient is increased, the shear stress is intensified near the bundary, mre turbulence is generated and the turbulent kinetic energy increases, s the heat transfer between the fluid and the wall is enhanced. Jacksn and Hall [13] intrduced nn-dimensinal buyancy effect parameter, B*, t evaluate the buyancy effect as: B Gr = Re Pr.8 (18) Where, B* 1E-6 1E-7 1E-8 1E-9 1E kw. m kw. m kw. m kw. m kw. m kw. m kw. m kw. m (b) G=4 kg m -2 s T f / Gr = g pd 4 i 2 (19) Re = Gd (2) Accrding t McEligt and Jacksn [29], the buyancy effect is negligible fr B* < fr bth upward and dwnward flws. Fr upward flws with < B* < , the buyancy reduces the heat transfer while fr < B* < 8 1 6, the heat transfer reductin gradually decreases as the B* increases, but the buyancy still negatively affects the heat transfer. Fr B* > the buyancy enhances the heat transfer. Fr dwnward flw, the buyancy will always enhance the heat transfer fr B* > The buyancy effect n the heat transfer fr relatively high heat fluxes and large temperature differences is f great imprtance in develping third fluid cling system using R22 r ethanl. Because the buyancy is mainly induced by the density variatins with temperature, R22 is expected t be mre influenced by the buyancy effects than ethanl since the R22 density variatins are relatively large within the parameter ranges cnsidered here. The lcal wall temperature variatins with enthalpy fr varius heat fluxes fr upward and dwnward flws at p = 5.5 MPa and G = 2 kg m 2 s 1 fr R22 are cmpared in Fig. 19. When the heat flux is relatively lw, the lcal wall temperature increases with the enthalpy, whereas fr high heat fluxes, lcal maximum wall temperatures are bserved fr bth the upward and dwnward flw cases. The wall temperature variatins in the upward and dwnward flws are cnsistent with each ther and the differences are quite small, which indicates that the buyancy effect n the heat transfer is insignificant. Althugh the radial density variatin in the tube is significant due t the large temperature difference between the fluid and the wall, especially when the fluid changes frm the Fig. 2. Lcal B* fr varius heat fluxes. R22, p = 5.5 Mpa. Slid line: fluid temperature; dash dt line: pseud critical temperature fr 5.5 MPa. liquid-like state in the cre t the highly gas-like state adjacent t the wall in the radial directin, the lcal heat transfer decreases due t the high temperature fluid near the wall. Nevertheless, the Reynlds number is high due t the large mass flux despite the small channel size, which reduces the inhibitry effect f the buyancy n the turbulence near the wall; thus, the differences due t the buyancy fr the upward and dwnward flws are insignificant. The crrespnding nn-dimensinal buyancy parameter, B*, variatins with the enthalpy fr varius heat fluxes at p = 5.5 MPa and G = 2 kg m 2 s 1 fr R22 are shwn in Fig. 2(a). When the fluid temperature is belw T pc (the crrespnding enthalpy i pc = kj kg 1 ), B* increases with the heat flux, reaches a maximum near T pc and decreases drastically with the enthalpy when the fluid temperature exceeds T pc. B* decreases when the mass flux is increased t G = 4 kg m 2 s 1 as shwn in Fig. 2(b). B* is belw 1 7 fr all the experimental cnditins used in the present study. The experimental results are cnsistent with the McEligt and Jacksn criteria [29] that the buyancy is insignificant when B* < Influence f flw acceleratin The fluid expands as the temperature increases and pressure decreases alng the tube during heating and accelerates t maintain cntinuity; thus, the axial pressure gradient increases as a result. The shear stress in the vicinity f the wall will be reduced t balance the increased pressure gradient, s the turbulence near the wall is suppressed. The flw may even be laminarized when the flw acceleratin is strng, which means that althugh the flw