Heat Transfer to Sub- and Supercritical Water at Low Mass Fluxes: Numerical Analysis and Experimental Validation

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1 Heat Transfer to Sub- and Supercritical Water at Lo Mass Fluxes: Numerical Analysis and Experimental Validation Samuel O. Odu a, Pelle Koster a, Aloijsius G. J. van der Ham a,*, Martin A.van der Hoef b, Sascha R. A. Kersten a a Sustainable Process Technology, Faculty of Science and Technology, University of Tente, Postbus 217, 7500 AE, Enschede, The Netherlands. * a.g.j.vanderham@utente.nl Fax: b Physics of Fluid Group, Faculty of Science and Technology, University of Tente, Postbus 217, 7500 AE, Enschede, The Netherlands. Heat transfer to supercritical ater (SCW floing in a vertical heated tube and cooled annulus at lo mass fluxes (G<20 kg/m 2.s has been numerically investigated in COMSOL Multiphysics and validated ith experimental data. The turbulent models in COMSOL have been checked under conditions here experimentally derived heat transfer correlations are available, and it is concluded that the Shear-Stress Transport (SST turbulence model gives the most accurate results. Numerical results obtained sho buoyancy induced circulation of the fluid from the all into the bulk as ell as a thin thermal boundary layer at the inner all ith a steep temperature gradient and a flat temperature profile in the bulk fluid. In addition, the heat transfer coefficient of SCW is enhanced near the pseudo-critical temperature (T pc, and is deteriorated at temperatures above T pc. From the results of to-dimensional simulations, a ne heat transfer correlation for sub- to supercritical ater flo at lo mass fluxes has been developed. Temperature predictions using the proposed heat transfer correlation for SCW flo in a heated tube matches our experimental data. INTRODUCTION Supercritical ater SCW has been used as a reaction medium for the conversion of biomass to hydrogen and natural gas [1, 2], liquid fuels [3], for the total oxidation of hazardous materials (supercritical ater oxidation SCWO- [4-7] as ell as organic synthesis. SCW has been proposed as a coolant for nuclear reactors alloing for high heat transfer and increased thermal efficiency [8]. SCW also has potential in desalination for the production of drinking ater ith zero liquid discharge [9]. Supercritical ater processes are energy intensive, therefore in order to make supercritical ater processes a commercial success, heat integration is required to regain as much energy as possible from the process. To achieve this, the feed stream is heated by the supercritical product stream in a heat exchanger that operates at sub- to supercritical ater conditions. In this heat exchanger, the feed ill turn supercritical and the product stream ill become liquid (subcritical resulting in changes in properties such as the density, viscosity, heat capacity and thermal conductivity, hich influences the heat transfer characteristics [10]. Currently, most research on SCW heat transfer is focused on using SCW as a coolant in large scale nuclear reactors, hich requires high mass fluxes (G > 200 kg/m 2.s [8, 11-14]. Hoever, for designing pilot plant scale SCW processes such as supercritical desalination and supercritical ater gasification it is desirable to kno the heat transfer characteristics of SCW at lo mass fluxes (typically G < 20 kg/m 2.s. At these lo mass fluxes (mostly laminar flos Re < 2300, heat transfer may be either deteriorated or enhanced due to natural convective forces, hich do not play an active role at high mass fluxes (turbulent flos [14]. 1

2 In general, essential insights on the heat transfer characteristics as ell as an engineering correlation for heat transfer in supercritical ater at these lo mass fluxes necessary for designing heat transfer equipment for pilot scale supercritical ater processes are lacking. The goal of this paper is to provide these insights by numerical simulation and experimental validation. First, a 2D model is set up in a commercial CFD package, COMSOL Multiphysics (hich e hereafter denote as COMSOL and calculations are performed to determine if the model can accurately describe temperature profiles and heat transfer for flo conditions ith knon Nusselt correlations. Next, 2D simulations are performed for up-flo of ater in a heated vertical tube and don-flo of ater in a cooled shell annulus under supercritical conditions to calculate the flo patterns, temperature profiles as ell as heat transfer coefficients. The results of the 2D model for the up flo in a heated tube are validated ith experiments in a nely designed apparatus. The influence of natural convection is also studied and discussed. Finally, 1D Nusselt correlations for engineering design are proposed and validated ith experiments. GOVERNING EQUATIONS The equations that describe a steady, compressible to-dimensional flo follos from the las of conservation of mass, momentum and energy [15, 16]. The mass and momentum equations, Eqs. (1 and (2 respectively, represents the stationary Reynolds Averaged Navier- Stokes (RANS equations for turbulent flos. (ρu = 0 (1 ρ(u u = ( pi + [(μ + μ T ( u + ( u T 2 3 (μ + μ T(. ui] ( 2 ρki + F (2 3 The volume force vector, F, accounts for the gravity force that act donards in the z- direction. F = [ F r ] = [ 0 F z ρg ] (3 The conservation of energy is described by: here λ eff is the effective thermal conductivity. ρc p u. T = (λ eff T (4 Turbulence modelling Although the radial-averaged Reynolds number for the lo flux SCW heat transfer model is expected to be belo 2300 (i.e. laminar flo, some local turbulence is expected due to the increased flo near the all caused by natural convection. It is therefore necessary to include an accurate turbulence model in the COMSOL simulations. In COMSOL, there are various types of RANS turbulence models available. In order to determine hich turbulence model ill best represent our system, preliminary simulations ere carried out in COMSOL in three flo regimes here correlations are available in literature: laminar and turbulent flos under normal temperature and pressure conditions, and turbulent supercritical ater flo. The Shear-Stress Transport (SST turbulence model as found to give the most accurate results in these flo regimes, and as therefore chosen as the turbulence model for further simulations. For more information on the SST model, see [16] and [17]. The heat flux in Eq. (4 is modelled using the Kays-Craford heat turbulence model [18]. The turbulence model takes into account the contribution of turbulent fluctuations to the 2

3 temperature field. See [18] for detailed explanation of the Kays-Craford heat turbulence model. Natural convection Natural convection is produced by buoyancy forces. When temperature differences are introduced through boundaries maintained at different temperatures, the resulting density differences ill induce motion; hot fluid tends to rise and cold fluid tends to fall [19]. When both forced and natural convection are present in a system, this is called mixed convection [14]. There are to types of mixed convection: (i aiding flo, hen natural convection acts in the same direction as forced convection, and (ii opposing flo, here natural convection acts in the opposite direction to forced convection [14]. In this paper only aiding flo ill be considered. This means that heated flos are upards and cooled flos donards (see Figure 1. Natural convection is modelled ith Eq. (3. Post-processing The post-processing of the results consists mainly of averaging the 2D solutions hich are functions of the r- (radial and z- (axial directions to obtain 1D results hich are dependent on the z-direction. The average temperature of the fluid is determined by the mixing cup temperature and is calculated using Eq. (5. T mc (z = R o 2πr G(r, z C p(r, z T(r, z dr R i R o (5 2πr G(r, z C p (r, z dr R i The other temperature that is important is the temperature of the fluid at the inside all T i. The 1D averaged fluid properties are evaluated at the operating pressure and T = T mc, resulting in ρ mc, C p,mc, etc. (a (b Figure 1. Geometry of heated tube (a and cooled shell annulus (b models respectively. Table 1. Parameters and dimensionless numbers. Tube Shell G (kg/m 2.s 3.0, 7.0, , 7.0 P (bar T in ( C 27, 127, T o ( C , d t, d h (cm 1, Re Gr 3*10 6-6*10 9 4*10 4-8*10 6 Pr RESULTS OF THE HEATED TUBE MODEL Results obtained from the heated tube simulation ith G t = 7 kg/m 2.s, d t = 1 cm, T in = 327 o C and T o = o C (from here on referred to as the heated tube base case. See Table 1 for the simulation parameters are discussed. The obtained velocity profile and temperature profile for the steady state simulation are shon in Figure 2(a and (b respectively. These images are shon ith a distorted aspect ratio in order to display the full 3

4 fluid domain. In Figure 2(a, the colours represent the logarithm of the velocity magnitude (Eq. (6, hereas the arros indicate the direction of flo (but not the velocity magnitude. u log = log 10 (u mag /u in (6 An increased velocity near the all (about ten times the inlet velocity is observed. This is a direct result of the fluid heating up and consequently decreasing in density and viscosity. This gives rise to natural convection accelerating the fluid in the upard direction near the all, and thus decreasing the velocity in the bulk. Natural convection induced mixing also creates some circulation aay from the all, into the bulk of the fluid. At the beginning of the heat transfer area (z = 0, the incoming fluid comes in contact ith the circulating and/or stagnant bulk and is (abruptly transported to the all. It is reasonable that the fluid ill prefer to move close to the all as it presents the path of least resistance to flo. The band of lo velocity magnitude stretching from z = 0 to z = 70 (yello band can be explained by the fact that the velocity magnitude is governed mainly by the axial velocity hich is almost zero (horizontal arros in this region. The surface plot of the temperature profile is shon in Figure 2(b. A flat temperature profile is observed in the bulk indicating that the circulation flo increases mixing in the bulk. In addition, a boundary layer for temperature is observed at about 0.5 mm from the heated surface. The fluid in this thermal boundary layer is heated by thermal conduction, and as a result rises up the tube. At the same time, the fluid outside this boundary layer drifts toards the heated all as the hot boundary layer entrains more fluid through the action of viscosity (as shon in Figure 2(a. The radial temperature profile can be seen more clearly in Figure 3(a. The temperature from the outer tube all to the tube centre at three different axial position is plotted against the tube radial coordinates. A radial temperature gradient is observed only in the region 0.5 mm aay from the tube inner all. The temperature gradient in the boundary layer as ell as the thickness of the boundary layer is observed to increase ith increasing axial position. (a (b Figure 2. Velocity profile of heated tube base case (a: colour is based on Eq. (6, and arros sho direction and temperature profile (b. Fluid is r = cm, all is r = cm. Figure 3(b shos the heat transfer coefficient (HTC, tube inner all temperature and the tube centre temperature as function of the axial position. The HTC is observed to go through a peak (2750 W/m 2.K at 389 o C, then decreases rapidly to about 300 W/m 2.K. 4

5 (a (b Figure 3. Radial temperature profiles at z = 20, 60 and 80 cm respectively (a and tube inner all and centre temperatures and HTC profile as function of axial position for heated tube base case. This shos a deteriorated heat transfer in SCW in laminar flo at temperatures above the pseudo-critical temperature. Above the pseudo-critical temperature, the properties of supercritical ater becomes more gas-like under isobaric conditions. This could account for the deteriorated heat transfer coefficient obtained at these temperatures. Similar results ere obtained for the cooled shell annulus simulations. Nusselt correlations Local Nusselt numbers obtained from the 2D COMSOL models are fitted to other dimensionless numbers (Gr, Re, Pr and fluid properties. The parameters and dimensionless numbers that have been used for the data fitting are shon Table 1. We have fitted our data to the correlation proposed by Mokry et al. [8]: Nu = a Gr b Pr c Re d ( ρ e ( C g p, ( λ f ( μ h (7 ρ mc C p,mc λ mc μ mc Which includes the effect of forced convection (Re, natural convection (Gr and fluid properties (Pr, as ell as a correction factor based on the difference in material properties beteen the fluid in the bulk (mixing cup average and the fluid at the all. In Eq. (7, a h represent the fit parameters. The Nusselt fits obtained for the heated tube (Nu t and cooled shell annulus (Nu s are shon in Eqs. (8 and (9 respectively. The effect of diameter in Reynolds and Grashof has been taken into account in the Nusselt correlation for the heated tube by fitting to results obtained from simulations in to tube diameters (1 and 2 cm respectively. The Nusselt correlations fit ithin ±20%. Nu t = h td t λ mc,t = 0.81 Gr 0.33 Re Pr 0.06 ( C p, C p,mc Nu s = h sd h λ mc,s = 1.51 Gr 0.31 Re Pr 0.04 ( C p, C p,mc EXPERIMENTAL VALIDATION In order to validate the results of the 2D COMSOL simulations as ell as the obtained 1D Nusselt correlation for the heated tube, an experimental apparatus has been designed and constructed. Temperature measurements at different radial and axial positions in ater floing at sub- and supercritical conditions has been obtained ( ρ 0.24 ρ mc ( ρ 1.10 ρ mc (8 (9

6 The schematics of the experimental apparatus is shon in Figure 4. The main part of the apparatus consists of a stainless steel tube (ith an inner diameter of 2.14 cm, outer diameter of 3.41 cm and length 154 cm fitted ith 8 aluminium heating blocks that keep the tube outer all at a pre-set temperature. The heating blocks are insulated from the environment ith stone ool to reduce heat losses. Nine thermocouples (Ti1-Ti9, held at different radial positions, but at the same axial position by a movable thermocouple holder measure the radial temperature profile in the tube at different heights. The experimental apparatus can be operated at pressures up to 350 bar, and temperatures up to 500 o C. Measurements are carried out at tube axial positions 24, 44, 64, 84, 104, 124 and 144 cm respectively. Test conditions (summarized in Table 2 are modelled in COMSOL ith tube dimensions, mass flo, pressure, inlet temperature and outer all temperature profile (all obtained from experiment as model input parameters. Table 2. Test conditions for validation of 2D COMSOL model and 1D Nusselt correlation. Case A Case B m (kg/hr G (kg/m 2.s P (bar T in ( C T o ( o C Figure 4. Schematics of the heated tube experimental apparatus. The radial temperature profiles for cases A and B at tube length 44 cm and 84 cm are presented in Figure 5. The experimental results sho a flat radial temperature profile in the fluid ith a steep gradient at near-all regions. The comparison of the numerical simulation results ith the experimental data shos good agreement. This is proof that the 2D COMSOL model is accurate for SCW flo at lo mass fluxes. The derived 1D Nusselt correlation for the heated tube model has also been validated. A 1D heated tube as modelled in matlab ith the test conditions listed in Table 2 as input parameters. The results of the 1D validation for cases A and B are presented in Figure 6(a and (b respectively. In addition to the experimental results and the prediction from the proposed Nusselt correlation, predictions obtained using: the VDI heat atlas [20] correlation for free convection, the Sieder-Tate [15] correlation for forced convection, the correlation of Mokry et al. [8] for turbulent supercritical ater flo and results of 2D COMSOL simulations are also shon. 6

7 Figure 5. Comparison of radial temperature profiles obtained from 2D COMSOL simulation ith experimental data for test cases A and B. Results obtained ith the Sieder-Tate and Mokry correlations significantly under-estimate the experimental data. These correlations derived for turbulent flos here forced convection is the governing mechanism for heat transport are not suitable for conditions here natural convection governs heat transport mechanism. Although the VDI correlation performed much better than the forced convection correlations, it also under-predicts the measured temperature profiles. The VDI correlation has been derived for free convective flos under normal conditions of pressure and temperature and therefore cannot be applied to flos at sub- and supercritical conditions. The comparison of the experimental data ith the predicted mixing cup temperature obtained from the proposed Nusselt correlation and the results of the 2D COMSOL simulations sho a good match. (a (b Figure 6. Experimental outer all and mixing cup temperatures, and mixing cup temperature obtained from various Nusselt correlation for case A (a and case B (b respectively. CONCLUSIONS A numerical study has been carried out in COMSOL Multiphysics CFD package to provide more insights on heat transfer characteristics of supercritical ater floing at lo mass fluxes (G < 20 kg/m 2.s in a heated tube and cooled shell annulus. Different turbulent models (k ε, k ω, and SST ere tested under conditions for hich empirical heat transfer correlations are available. From these tests, it is concluded that the SST turbulence model gives the most accurate results. 2D models for a heated tube up-flo and cooled shell annulus don-flo have been solved and analysed. For the heated tube model, an increased fluid velocity (about 10 times the inlet velocity near the all and a decreased velocity of the fluid in the bulk are observed. This creates a natural convection induced circulation from the all into the bulk hich increases mixing and heat transfer. The heat transfer coefficient goes through a peak as the temperature of the fluid approaches the pseudo-critical temperature, then decreases rapidly at temperatures 7

8 above the pseudo-critical temperature. Similar results are obtained for the cooled shell annulus model. The 2D numerical results have been used to derive 1D Nusselt correlations for a heated tube and a cooled shell annulus that can be used for engineering calculations. Radial fluid temperatures of SCW flo at lo mass fluxes in a heated tube have been successfully measured in a nely designed experimental apparatus at different axial positions. The numerical results are in good agreement ith our experimental data. Temperature profiles obtained by using the proposed Nusselt correlation in a 1D heated tube model have been compared to experimental data and some correlations for free and forced convection published in literature. The results of the proposed Nusselt correlation and the 2D COMSOL model for the heated tube sho a good match ith our experimental data. Our proposed correlation can be applied in the design of heat transfer equipment for supercritical ater processes at lo mass fluxes. REFERENCES 1. Kersten, S.R.A., et al., Gasification of Model Compounds and Wood in Hot Compressed Water. Ind. Eng. Chem. Res., : p Kruse, A., Hydrothermal biomass gasification. The Journal of Supercritical Fluids, (3: p Schacht, C., C. Zetzl, and G. Brunner, From plant materials to ethanol by means of supercritical fluid technology. The Journal of Supercritical Fluids, (3: p Bermejo, M.D. and M.J. Cocero, Supercritical ater oxidation: A technical revie. AIChE Journal, (11: p Brunner, G., Near and supercritical ater. Part II: Oxidative processes. The Journal of Supercritical Fluids, (3: p Qian, L., S. Wang, and J. Zhang, Experimental study on supercritical ater oxidation of paper mill sludge. Adv. Mater. Res. (Durnten-Zurich, Sitz., : p Chen, Z., et al., A ne system design for supercritical ater oxidation. Chemical Engineering Journal, : p Mokry, S., et al., Development of supercritical ater heat-transfer correlation for vertical bare tubes. Nucl. Eng. Des., : p Odu, S.O., et al., Design of a Process for Supercritical Water Desalination ith Zero Liquid Discharge. Industrial & Engineering Chemistry Research, (20: p Wagner, W., et al., The IAPWS industrial formulation 1997 for the thermodynamic properties of ater and steam. J. Eng. Gas Turbines Poer, : p Bishop, A.A., F.J. Krambeck, and R.O. Sandberg, High-temperature supercritical pressure ater loop. III. Forced convection heat transfer to superheated steam at high pressure and high Prandtl numbers, 1964, Westinghouse Elec. Corp. p. 101 pp. 12. Senson, H.S., J.R. Carver, and C.R. Kakarala, Heat transfer to supercritical ater in smooth-bore tubes. J. Heat Transfer, : p Yamagata, K., et al., Forced convective heat transfer to supercritical ater floing in tubes. Int. J. Heat Mass Transfer, : p Aicher, T. and H. Martin, Ne correlations for mixed turbulent natural and forced convection heat transfer in vertical tubes. Int. J. Heat Mass Transfer, : p Bird, R.B., W.E. Steart, and E.N. Lightfoot, Transport Phenomena. Revised Second ed. 2007, Ne York: John Wiley & Sons, Inc. 16. Versteeg, H.K. and W. Malalasekera, An Introduction to Computational Fluid Dynamics - The Finite Volume Method. Second ed. 2007, London: Pearson Education Limited. 17. Menter, F.R., M. Kuntz, and R. Langtry, Ten Years of Industrial Experience ith the SST Turbulence Model, in Turbulence, Heat and Mass Transfer 4, K. Hanjalic, Y. Nagano, and M. Tummers, Editors. 2003, Begell House, Inc. p Kays, W.M., M.E. Craford, and B. Weigand, Convective Heat and Mass Transfer. Fourth ed. 2005, Singapore: McGra-Hill. 19. Tritton, D.J., Physical Fluid Dynamics. Second ed. 1988, Oxford: Clarendon Press. 20. Kast, W. and H. Klan, Heat Transfer by Free Convection: Special Cases, in VDI Heat Atlas, V.-G.V.u.C. (GVC, Editor 2010, Springer-Verlag Berlin Heidelberg: Heidelberg. p