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Heat transfer deterioration in a supercritical water channel
Nuclear Engineering and Design 240 (2010) 3321–3328
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Heat transfer deterioration in a supercritical water channel Min-Tsung Kao, Min Lee ∗ , Yuh-Ming Ferng, Ching-Chang Chieng Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30043, Taiwan
a r t i c l e
i n f o
Article history: Received 3 February 2010 Received in revised form 12 June 2010 Accepted 21 June 2010
a b s t r a c t Supercritical water is the working fluid in the supercritical water reactor (SCWR) because of its high thermal efficiency and simplicity. Computational fluid dynamics (CFD) technology has been applied in the studies of supercritical water in circular channels by solving conservation equations of mass, momentum, and energy. Both the renormalization group k-(RNG k-) and Reynolds stress equation model (RSM) turbulence models were applied with enhanced wall treatment (EWT) for Yamagata’s heat transfer enhancement (HTE) experiments. Reynolds Stress turbulence model (RSM) with the enhanced wall treatment (EWT) was used for diagnosis and comparison of the heat transfer deterioration (HTD) phenomena observed in the Shitsman’s experiments. The simulations confirmed the heat transfer deterioration (HTD) phenomenon and predicted the associated peak wall temperature and minimum heat transfer coefficient consistent with Shitsman’s experiment. Series simulations with various operational pressures and inlet temperatures (Tin ) indicated that the increases of both inlet temperature and operational pressure were very effective to relax the heat transfer deterioration. The inclusion of buoyancy effect in the physical model revealed that the buoyancy effect played role on the dramatic increase of the wall temperature, which indicated the important role of buoyancy force on HTD by limiting the convection and turbulence. Dimensionless parameter of Prandtl number, the ratio of momentum and energy diffusion, which changing dramatically near the wall with wide range from 0.8 to 16.6, led to very different patterns of momentum and energy transports in the small region and was another important parameter for the formation of HTD. This study concluded the important roles of buoyancy effect and Prandtl number on heat transfer deterioration of supercritical water inside circular tubes. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Supercritical water reactor (SCWR) is a potential candidate of the Gen IV systems because of its high thermal efficiency (45%) and highly simplified plant systems. The major concern using supercritical water as work fluid is the heat transfer characteristics due to large variations of thermal properties of supercritical water near pseudo-critical line (Fig. 1). It is well known that deterioration in heat transfer for supercritical fluid flowing vertically upward in a tube occurs at a high heat flux. The criterion of the onset of heat transfer deterioration for gas flow in the small diameter tube has been examined in the experimental data [1–4] and suggested an acceleration parameter Kv measuring laminarization and a Buoyance parameter Bo* determining the onset of buoyancy influence. Lee et al. [5] collected experimental data for nitrogen, helium and carbon dioxide and updated the traditional thresholds of the deteriorated turbulent heat transfer (DTHT) regimes in circular tube.
∗ Corresponding author. Tel.: +886 3 572 917; fax: +886 3 572 0724. E-mail address: [email protected] (M. Lee). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.06.028
Since the dependence of thermo-physical properties between the gas and supercritical fluid is very different, it is not appropriate to apply the criteria from gas flow to supercritical water. Shiralkar and Griffith [6] determined both theoretically (for supercritical water) and experimentally (for supercritical carbon dioxide) the limits of maximum heat flux for a particular mass flux and found that the heat transfer deterioration (HTD) occurred when the bulk fluid temperature was below and the wall temperature above the pseudo-critical temperature. A series of overview of the existing criteria have been presented by Pioro and Duffey [7], Cheng and Schulenberg [8], Anglart [9] and indicated the large differences. A number of review papers on supercritical water studies in 1970s and 1980s [10–15] had been reported including numerical analysis as well as experimental works and empirical correlations. Some of the experiments observed no heat transfer deterioration [16,17] but Shitsmann [13], Ornatskij et al. [15] and Yamagata et al. [12] did. In the literatures, there are several explanations and debates for the mechanism of heat transfer deterioration. They indicated that HTD can be caused by rapid variation of thermophysical properties, acceleration, buoyancy effect or combination of these phenomena [1,2,18]. Palko and Anglart [19] had studied
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Nomenclature Cp [KJ/kg K] fluid specific heat G [kg/m2 s] mass flux I [%] turbulent intensity P [MPa] operating pressures Pr [–] Prandtl number q [kW/m2 ] wall heat flux r [m] radial direction in cylindrical coordinates T [K] fluid temperature TC [K] temperature at central axis T −T T* [–] dimensionless temperature T ∗ = q / CpC u i
i i
u [m/s] velocity u* [–] dimensionless velocity, u/ui z [m] axial direction in cylindrical coordinates ˛ [m2 /s] thermal diffusivity [m2 /s] momentum diffusivity [kg/m3 ] density Subscripts C central axis i inlet condition
the influence of buoyancy and thermo-physical properties variations on heat transfer to supercritical water. They found that the influence of buoyancy forces was significant at low mass flow rates to create HTD. However, the designated mass flow for SCWR is high enough to neglect the buoyancy force. At high mass flow rates, a low-conducting layer close to the heated wall was created due to the variation of thermal conductivity and this layer acted as a thermal barrier causing the onset of HTD. Thus, heat transfer of supercritical water using CFD analysis has been of interest to analyze and to understand physical mechanism. The main difficulties in numerical analysis are: (1) the choice of turbulence model, (2) buoyancy effect and acceleration effect due to the large variation of thermal properties, (3) the significant change of Prandtl number at pseudo-critical condition. Most of CFD analyses were successful on the study of heat transfer enhancement for supercritical water near pseudo-critical line and the computation experiences can be extended to study heat transfer deterioration. Kim et al. [10] used all the first order of turbulence models and six low-Reynolds turbulence models to study the heat transfer enhancement phenomenon and compared the results with Yamagata et al.’s experiment. He had a big success in using the renormalized group (RNG) turbulence model with
Fig. 1. Thermal properties of supercritical water at 23.3 MPa.
Fig. 2. Schematic diagram of solution domain and the applied boundary conditions: (a) Yamagata’s HTE and (b) Shitsman’s HTD experiments.
enhanced wall treatment (EWT) to predict Yamagata et al.’s experiment data. Nevertheless, in complicated geometry, like the rod bundle in reactor, first order of turbulence model cannot predict the secondary flow very well. Roelofs [14] used the second order turbulence model, Reynolds stress model (RSM) with EWT and also studied the heat transfer of supercritical water in Yamagata et al.’s experiment. He found RSM turbulence can predict the experimental data well than RNG did. Roelofs also discussed the effect of y+ value of first layer grid near the wall when simulating heat transfer of supercritical water and he suggested that y+ should be lower than 1. Furthermore, Roelofs predicted the mass flux and the corresponding heat flux for an onset of heat transfer deterioration without detailed descriptions of the phenomenon. Present study will study heat transfer deterioration in terms of the associated wall peak temperature and heat transfer coefficients using CFD analysis and compare with Shitsman’s experiment [13] to identify the physical phenomenon of heat transfer deterioration (HTD) for supercritical water and the effects by inlet temperature and operational pressure as well as the formation of HTD. In additional, the progress of HTD is illustrated by dimensional parameters for the progress of HTD and the recovering of heat transfer. 2. Physical and numerical model In the present paper, simulations are conducted for both heat transfer enhancement and deteriorations. The simulations for heat transfer enhancement not only provide the comparison against Yamagata’s HTE experiment but also the applicability of the computer code to both HTE and HTD problems. Yamagata et al. [12] studied heat transfer phenomenon (both HTE and HTD) as supercritical water flows in circular tube (diameter = 7.5 mm) with a range of parameters: operation pressure from 226 to 294 bar, applied heat flux (q ) from 116 to 930 kW/m2 and mass flux (G) from 310 to 1830 kg/m2 s. Present study chose the case of supercritical water flowing upward with q = 233 kW/m2 and G = 1260 kg/m2 s as the benchmark data for the simulations. Fig. 2(a) illustrates the schematic diagram of solution domain for Yamagata’s Experiment. Shitsman [13] studied the heat transfer deterioration phenomenon of supercritical water through circular pipe flow with five different heat fluxes applied on pipe wall. In the present study, the benchmark data for HTD is chosen from the cases of circular channels with radius 0.4 cm. The channel consists of 3 sections: unheated–heated–unheated sections at 0.6–2.9–0.4 m (Fig. 2(b)).
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Fig. 3. The mesh configuration for simulating (a) HTE and (b) HTD.
The experimental conditions undergoing heat transfer deterioration are with the mass flow rates of 430 kg/m2 , inlet temperature at 597.4 K, at operation pressure of 23.3 MPa, with wall heat flux of 386.134 kW/m2 applied on heated section and at Reynolds number ranging from 4.38 × 104 to 8.6 × 104 . The properties near pseudocritical conditions are varied sharply for supercritical water. The simulations are performed using thermal properties table from the National Institute of Standards and Technology (NIST) Chemistry webbook [20]. Non-slip and constant heat flux are the boundary conditions on wall for both HTE and HTD simulations. 2.1. Governing equations and turbulence model In this study, distributions of flow, temperature fields, and turbulent intensity as well as Prandtl number in the computational domain were obtained by solving the equation of continuity, energy, and momentum with Reynolds stress turbulence model
Fig. 5. Computed (a) wall temperature (b) heat transfer coefficient compared with Shitsman’s experiment at Tin = 597.4 K, P = 23.3 MPa.
(RSM) or renormalization group k-(RNG k-) [21]. RSM, known as second-moment closure model, closes the Reynolds-averaged Navier–Stokes equations by solving additional transport equations for the Reynolds stresses. The isotropic eddy viscosity assumption used in standard k- equation [21] is removed by using RSM. RSM can account for the effects due to streamline curvature, swirl, rotation, high strain rates, and secondary flow in ducts. Enhanced wall treatment is applied on near-wall region, which is a near-wall modelling approach that combines a two-layer model with enhanced wall functions. The near-wall mesh is fine enough to be able to resolve the laminar sublayer with first node of y+ near 1, then the enhanced wall treatment is identical to the traditional two-layer zone method. 2.2. Grid generation The thermal properties of supercritical water, like density, specific heat, viscosity and thermal conductivity, vary dramatically as approaching to the pseudo-critical conditions. Thus, very fine mesh is required to resolve the heat transfer phenomenon at nearwall region at temperature near the critical point. Furthermore, the application of enhanced wall treatment needs very fine grid near wall (y+ ∼ 1).
Fig. 4. Heat transfer coefficient versus bulk temperature.
2.2.1. Computational grid for Yamagata’s HTE experiment Fig. 3(a) shows the schematic diagrams of the computational meshes with 30 grids in r direction with successive ratio of 1.2. The y+ ranges from 1.2 to 2.5 at first grid near the wall for solving Yamagata’s HTE Experiment. Grid independence tests were conducted with different node numbers in the axial direction, i.e. node numbers were 20, 30, and 40 with the total node numbers of 55,000, 82,500 and 110,000, respectively. Less than 1% difference was observed between the grids of 82,500 and 110,000 nodes.
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Fig. 6. 15 Simulation results compared with Shitsman’s experiment at Tin = 597.4 K (a), (c) and (e) wall temperature and (b), (d) and (f) heat transfer coefficient.
2.2.2. Computational grid for Shitsman’s HTD experiment Fig. 3(b) shows that a 30 uniform prism layer is generated at distance 0.0075 cm from wall (i.e. radial position ranging from 0.3925 to 0.4 cm) and 60 grids are generated in region of radius less than 0.3925 cm with successive ratio of 1.08. The total mesh size is 540,000 with y+ ranging from 0.2 to 0.925 at first grid near the wall. Since the temperature gradient near the heated wall for the HTD case is sharper than that for the HTD case, much more grids were applied near heated wall region to avoid the grid dependence (i.e. 30 more nodes at the first node compared in HTE case). 3. Results The simulations are conducted for both heat transfer enhancement and deteriorations and are compared with experiments. The results are discussed in the following sections.
3.1. Yamagata’s HTE simulation The heat transfer enhancement is caused by the sharp increase of specific heat near the pseudo-critical temperature [22]. Good predictions on heat transfer coefficient versus bulk temperature (Tb ) are obtained using both turbulence models as shown in Fig. 4, except the slightly over-estimation of heat transfer coefficient and the shifted maxima near the pseudo-critical temperature (656.2 K). The maximum heat transfer coefficient is observed at Tb ∼ 655.4 K instead of at the pseudo-critical temperature (656.2 K) where the peak value of specific heat is occurred. The good prediction of HTE implies the capability of computations using Computer Software FLUENT and the adequacy of the grid system applied for supercritical fluid in circular channels.
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3.2. Shitsman’s HTD simulation Fig. 5 (a) and (b) plot the computed wall temperature and the heat transfer coefficient (h) versus weighted enthalpy at the cutting plane z, respectively. Since the enthalpy increases from inlet as heat flux applied in the heated section, the enthalpy has been chosen to replace the length along the Z direction and illustrated the results in the literatures. The observation confirms the heat transfer deterioration (HTD) phenomenon and captured the major physics. Nevertheless some discrepancies between the computed and measured wall temperature and heat transfer coefficient are shown. Considering uncertainty in measurements and the corresponding deviations in thermal properties at operation conditions, a set of additional 14 simulations have been conducted at different operation pressures and inlet temperatures. The operation conditions include five different operation pressures, 22.8, 23, 23.3, 23.4 and 23.9 MPa and 3 different inlet temperatures, 590, 597.4 and 603 K. 3.2.1. Effect of operational pressure on HTD With the same inlet temperature 590 K, Fig. 6 (a) and (b) shows the wall temperature variations and heat transfer coefficient along the flow direction at operating pressures (P) ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 859.8, 869, 877.8, 810.4, 765.9 K at operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 1.66, 1.59, 1.53, 2.15, and 2.96 kW/m2 K, respectively. It indicates the peak wall temperature of 877.8 K and a minimum heat transfer coefficient (HTD) of 1.53 kW/m2 K are occurred at bulk enthalpy of 1668 KJ/kg at P = 23.3 MPa for inlet temperature 590 K. As the inlet temperature is increased to 597.4 K, Fig. 6(c) and (d) shows the wall temperature variations and heat transfer coefficients along the flow direction at operating pressures ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 843.9, 862.1, 864.9, 792.9, 719.4 K at operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 1.81, 1.65, 1.63, 2.42, and 4.49 kW/m2 K, respectively. It indicates that the peak wall temperature of 864.9 K and a minimum heat transfer coefficient of 1.63 kW/m2 K are occurred at bulk enthalpy of 1685 KJ/kg at P = 23.3 MPa for inlet temperature 597.4 K. As the inlet temperature is further increased to 613 K, Fig. 6(e) and (f) shows the wall temperature variations and heat transfer coefficient along the flow direction at operating pressures ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 709.0, 753.4, 776.1, 704.6, and 704.9 K for operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 4.86, 3.35, 2.79, 5.08, and 5.10 kW/m2 K, respectively. It indicates that the peak wall temperature of 776.1 K and a minimum heat transfer coefficient of 2.79 kW/m2 K are occurred at bulk enthalpy of 1768 KJ/kg at P = 23.3 MPa for inlet temperature 613 K. Table 1 summarizes the minimum heat transfer coefficients, peak wall temperature for the series of the predictions at different operation pressures and inlet temperatures. The worst condition occurs at operation pressure of 23.3 MPa and temperature of 590 K, comparing the experimental conditions at 23.3 MPa and 597.4 K by Shitsmann. For inlet temperature of 597.4 K, Table 1 indicates that the most severe heat transfer deterioration occurs at P = 23.3 MPa with the minimum heat transfer coefficient of 1.63 kW/m2 K. Similar trend o is observed at Tin = 613 K. If operation pressure is raised from 23.3 to 23.4 MPa, the peak wall temperature is lowered from 877.8 to 810.4 K (67.4 degree, ∼7.7%), from 864.9 to 792.9 K (72 degree, ∼8.3%) and from 776.1 to 704.6 K (71.5 degree, ∼9.2%) for Tin = 590, 597.4 and 613 K respectively. It indicates that the
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Table 1 Predicted peak wall temperature (K) and minimum heat transfer coefficient h (kW/m2 K) for each simulation. Peak wall temperature and minimum heat transfer coefficient of each simulation case (peak wall temperature (K). Minimum heat transfer coefficient (kW/m2 K)) Operation P (MPa) Tin (K)
22.8 23.0 23.3 23.4 23.9
590
597.4
613
(859.8, 1.66) (869.0, 1.59) (877.8, 1.53) (810.4, 2.15) (765.9, 2.96)
(843.9, 1.81) (862.1, 1.65) (864.9, 1.63) (792.9, 2.42) (719.4, 4.49)
(709.0, 4.86) (753.4, 3.35) (776.1, 2.79) (704.6, 5.08) (704.9, 5.10)
operation pressure play an important role in heat transfer deterioration phenomenon at around 23.3 MPa. HTD is not observed at P = 23.4 MPa with Tin = 613 K (Fig. 6(e) and (f)). As the operation pressure is raised from 23.4 to 23.9 MPa at Tin = 590 K, the peak wall temperature decreases from 810.4 to 765.9 K (Fig. 6(a)), i.e. 5.5% change of the peak wall temperature with Tin = 590 K. Overall speaking, alleviation of heat transfer deterioration is observed for operation pressure higher than or equal to 23.4 MPa or inlet temperature as high as 613 K. 3.2.2. Effects of inlet temperature on HTD For operating pressure at 22.8 MPa, minimum heat transfer coefficient is recovered (or HTD is diminished) as the inlet temperature is increased from 590 to 613 K as comparing Fig. 5(a), (c) and (e). Similar observations are shown for the supercritical water operates at 23.0, 23.4 and 23.9 MPa also. For inlet temperature as high as 613 K, heat transfer deterioration is disappeared for all pressures except for 23.0 and 23.3 MPa (Fig. 6(e)). 3.2.3. Effect of buoyancy force on HTD Fig. 7 shows the simulation results of wall temperature with and without considering the effect of buoyancy force (gravity) under P = 23.3 MPa and Tin = 590 K. If the buoyancy effect is not taken into account, the wall temperature increases slowly along Z direction. However, as the buoyancy effect is considered in the simulation, wall temperature experiences a rapid rise and reaches a peak of wall temperature (877.8 K) at Z = 114.65 cm. It implies that the pseudocritical condition (651.75 K for P = 23.3 MPa) occurs at Z = 114.65 cm and r/R = 0.9 with fluid temperature at 626 K. This indicates that buoyancy effect plays an important role in heat transfer deterioration, which is very different from that in heat transfer enhancement [19].
Fig. 7. Wall temperature variation with/without Buoyancy effect considered on HTD.
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Fig. 8. Dimensionless parameters at section levels before and after HTD.
3.2.4. Discussion of HTD progress by dimensionless parameters The unheated section of the circular tube from Z = 0 to 60 cm allows supercritical water flow to be fully developed. With wall heat flux of 386.134 kW/m2 applied from Z = 60 to 350 cm, the supercritical water is heated with a sharp rise before it reaches the maximum temperature at Z = 114.65 cm (Fig. 7). Heat transfer deterioration is not severe at the section of Z = 70–100 cm but the apparent HTD is observed at Z = 105–130 cm. Heat transfer recovers and HTD diminishes after Z = 130 cm. Fig. 7 illustrates the wall temperature variations before, during, and after HTD. Wall temperature and heat transfer coefficients are related to the temperature gradient, velocity gradient, turbulent intensity, and the Prandtl number distribution near the wall. In this paper, the discussion of HTD progress will be based on two lines; (1) based against Prandtl number profile at individual Z-sections: correlating these profiles at chosen sections of Z = 90, 110, 114.65, 120 and 130 cm, and (2)
based on the increased of Z: illustrating the progress of the profiles of Prandtl numbers, mass flux, and turbulent intensity as flow approaching and leaving HTD (i.e. as Z increases). The distributions of non-dimensional parameters of temperature (T*), velocity (u*), turbulent intensity (I) against Prandtl number (Pr) at sections of Z = 90, 110, 114.65, 120 and 130 cm are shown in Fig. 8(a)–(e). These are the representative profiles showing the HTD progress in regions before HTD (e.g. Z = 90 cm), approaching HTD (e.g. Z = 110 cm), during HTD (e.g. Z = 114.65 cm) and after HTD (e.g. Z = 130 cm). At Z = 70 cm, Prandtl number (Pr) is nearly constant (0.8) except for a rise at very near-wall region (r/R > 0.99375), a moderate temperature gradient (T* ∼ 367), a relatively thick boundary layer, and a turbulent intensity level of ∼4% with a peak located at r/R ∼ 0.9875 are observed. At Z = 90 cm, the region of high Pr is expanded to a sharp peak, wall temperature (T* ∼ 560) with a sharp temperature decrease away from the wall
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Fig. 9. Progress of Prandtl number profiles (a) before and (b) after HTD. Fig. 11. Mass flux for P = 23.3 MPa, Tin = 590 K (a) r/R = 0–1 and (b) r/R = 0.975–1.
Fig. 10. Turbulent intensity I (%) for P = 23.3 MPa, Tin = 590 K (a) r/R = 0–1 and (b) r/R = 0.875–1.
is appearing, a wall peak of turbulent intensity (∼4%) exists, and a smooth velocity profile is observed. At Z = 110 cm where the HTD approaching with wider Prandtl number peak, wall temperature rise (T* ∼ 900), higher velocity, and a sharper wall peak of turbulent intensity with magnitude decrease (∼3%) are observed. As flow near HTD (Z = 114.65 cm), Prandtl number peak is wider and moves farther from wall, higher wall temperature (T* ∼ 1600), and lower turbulence intensity (∼2%) of narrower wall peak are correlated. As heat transfer recovered from HTD at Z = 120 cm, the Prandtl number profiles moves toward wall again, thinner velocity boundary layer, lower wall temperature (Tw * ∼ 760), and higher turbulence intensity wall peaks are recovered (∼4%). As flow leaving HTD with narrower Prandtl number peak, all these flow and temperature profiles are recovered. As the flow goes downstream, the peak of Prandtl number is moved away from the wall to where the largest velocity occurred and this is where the worst heat transfer happened (i.e. highest wall temperature and lowest heat transfer coefficient at Z = 114.65 cm) and then the higher momentum at very near-wall region can be transported out to speed up the whole fluid region and heat transfer becomes better. In all the simulation cases, Prandtl number ranges from 0.8 to 16.6. Since Prandtl number is the ratio of momentum and energy diffusion, the fluid region with Prandtl number much larger than 1 indicates the fluid experiencing much better momentum diffusion than energy diffusion and much thicker hydraulic boundary layer than thermal boundary layer as Fig. 9 shows. As the flow approaching the pseudo-critical point (Z = 110 cm), high Pr region is extended to r/R ∼ 0.9625 with peak located r/R ∼ 0.9925, turbulent intensity is reduced to 2–3% level (which is equivalent to laminarization as observed by previous studies (1–4)). Fig. 9(a) plots the progress of Prandtl number profiles before HTD, the regions of Prandtl number peak are increased as Z increases, the peaks are not only wider and higher but also moved away from the wall as flow approaching HTD.
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Fig. 10 plots the progress of turbulent intensity profile before and after HTD, the turbulent intensity decreases as approaching HTD and recovers after HTD, which implies the laminarization. The laminarization is also revealed by the profiles of mass flux near the wall (Fig. 11). Mass flux near wall decreases as flow approaching HTD and recovers after HTD. The decreasing of turbulent intensity deteriorates the heat transfer. At the sections near HTD, heat is accumulated at the fluid region between the heated wall and the peak of Prandtl number, thus the temperature difference T at this region increases. Larger temperature difference induces larger buoyancy force at very near-wall region. The buoyancy force increases the velocity and changes the velocity profile with smaller velocity gradient and smaller turbulent intensities at very near-wall region. (Fig. 10(a) and (b)). 4. Conclusions Heat transfer deterioration in supercritical water channel is studied by solving conservation laws of mass, momentum, and energy with Reynolds Stress turbulence model and enhanced wall treatment using CFD technology. The simulations confirm that the buoyancy effect in addition to laminarization play an important role resulting from large variations of thermal properties, which is very different from that in heat transfer enhancement. The simulation results confirmed the heat transfer deterioration phenomenon and captured the major physics although the location and magnitude of peak wall temperature were not perfectly predicted as compared with the Shitsman’s experiment data under the same operation condition. 15 simulations with 5 operational pressures and 3 inlet temperatures (Tin ) have been conducted and indicated that the increases of both inlet temperature and/or operational pressure were very effective to relax or relieve the heat transfer deterioration. Prandtl number is introduced and identified as a representing parameter of physical property to describe the progress of HTD. The enlarging region of high Prandtl number ranging from 0.8 to 16.6 as approaching HTD implies the high ratio of momentum diffusion compared to energy transport and thus the laminarization of turbulence. HTD is formed because the buoyancy force is confined at very near-wall region at the beginning of heating. This study concluded the important roles of buoyancy effect and Prandtl number on heat transfer deterioration of supercritical water inside circular tubes. Acknowledgement The authors highly appreciate the supports from the National Science Council, Taiwan under contract NSC98-3114-E-007-007. References McEligot, D.M., Coon, C.W., Perkins, H.C., 1970. Relaminarization in tubes. Int. J. Heat Mass Transfer 9, 1151–1152. Bankston, C.A., McEligot, D.M., 1970. Turbulent and laminar heat transfer to gases with varying properties in the entry region of circular ducts”. Int. J. Heat Mass Transfer 13, 319–344. Moretti, P.M., Kays, W.M., 1965. Heat transfer to a turbulent boundary layer with varying free-stream velocity and varying surface temperature—an experimental study. Int. J. Heat Mass Transfer 8, 1187–1202.
McEligot, D.M., Jackson, J.D., 2004. Deterioration criteria for convective heat transfer in gas flow through non-circular ducts. Nucl. Eng. Des. 232, 327–333. Lee, J.I., Hejzlar, P., Saha, P., Stahle, P., Kazimi, M.S., McEligot, D.M., 2008. Deteriorated turbulent heat transfer (DTHT) of gas up-flow in a circular tube: experimental data. Heat Mass Transfer 51, 3259–3266. Shiralkar, B.S., Griffith, P., 1970. The effect of swirl, inlet conditions, flow direction, and tube diameter on the heat transfer to fluids at supercritical pressure. J. Heat Transfer Trans. ASME 92 ((3) August), 465–474. Pioro, I.L., Duffey, R.B., 2005. Experimental heat transfer in supercritical water flowing inside channels (survey). Nucl. Eng. Des. 235, 2407–2430. Cheng. X., Schulenberg, T., 2001. Heat transfer at supercritical pressures—literature review and application to a HPLWR. Scientific Report FZKA6609, Forschungszentrum Karlsruhe. Anglart, H., 2009. Heat transfer deterioration in application to the HPLWR mechanisms identification and ranking table. In: Proceedings of the Fourth International Symposium on Supercritical Water Cooled Ractors, Heidelberg, Germany, March 8–11. Kim., S.H., Kim, Y.I., Bae, Y.Y., Cho, B.H., 2004. Numerical simulation of the vertical upward flow of water in a heated tube at supercritical pressure. In: Proceedings of ICAPP. Cheng, X., Kuang, B., Yang, Y.H., 2007. Numerical analysis of heat transfer in supercritical water cooled flow channels. Nucl. Eng. Des.. Yamagata, K., Nishikawa, K., Hasegawa, S., 1972. Forced convection heat transfer to supercritical water flowing in tubes. Int. J. Heat Mass Transfer 15, 2575–2593. Shitsman, M.E., 1963. Impairment of the heat transmission at supercritical pressures. High Temp. 1 (2), 237–244. Roelofs, F., 2004. CFD Analyses of heat transfer to supercritical water flowing vertically upward in a tube. Under the contract of the Netherlands Ministry of Economic Affairs. Ornatskij, A:P., Glushchenko, L.F., Kalachev, S.I., 1971. Heat transfer with rising and falling flows of water in tubes of small diameter at supercritical pressures. Thermal Engineering 18 (5), 137–141. Dickinson, N.L., Weich, C.P., 1958. Heat transfer to supercritical water. ASME 80, 745–751. Domin, G., 1963. Wärmeübergang in kritischen und überkritischen Bereichen von Wasser in Rohren. BWK 15 ((11) November). Mikielewicz, D.P., Shehata, A.M., Jackson, J.D., McEligot, D.M., 2002. Temperature, velocity and mean turbulence structure in strongly-heated internal gas flows—comparison of numerical predictions with data. Int. J. Heat Mass Transfer 45, 4333–4352. Palko, David, Anglart, Henryk, 2008. Numerical study of the influence of buoyancy and thermo-physical properties variations on heat transfer to supercritical water. In: The Seventh International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety Seoul, Korea, October 5–9. http://webbook.nist.gov/chemistry/fluid/. FLUENT 6.3 User’s guide. Renz, F.U., Bellinghausen, R., 1986. Heat Transfer in a vertical pipe at supercritical pressure. In: Eighth International Heat Transfer Conference, vol. 3, pp. 957–962. Mr. Min-Tsung Kao received his B.S. and M.S. degrees from the Department of Engineering and System Science of National Tsing Hua University (NTHU) of Taiwan at 2007 and 2009, respectively. He is serving his military duty for the country now. Prof. Min Lee received his B.S. and M.S. degrees in Nuclear Engineering from NTHU. He received his Ph.D. degree in Nuclear Engineering from Massachusetts Institute of Technology in 1985. Before he went back to NTHU and became a professor at Department of Nuclear Engineering in 1989, he had worked at Brookhaven National Laboratories for 3 and half years. His expertise includes thermal hydraulic analysis of nuclear power system, probabilistic safety assessment of nuclear Power Plant, and heat transfer. Prof. Yuh-Ming Ferng received his B.S. and Ph.D. degrees in Nuclear Engineering Department from NTHU at 1986 and 1990, respectively. Before he joined the Department of Engineering and System Science at 2008, he worked at Institute of Nuclear Energy Research of Atomic Energy Commission of Taiwan. His expertise includes computational fluid dynamics, turbulent flow, and CFD simulations of reactor components. Prof. Ching-Chang Chieng received her B.S. degree in Nuclear Engineering from National Tsing Hua University, Hsinchu, Taiwan, then she completed her M.S. degree in Chemical Engineering from University of Rhode Island, U.S.A. and Ph.D. in Aerospace and Ocean Engineering from Virginia Polytechnic Institute and State University, U.S.A. She joined Department of Engineering and System Science, National Tsing Hua University as a professor in 1981. Her expertise includes computational fluid dynamics, turbulent flow, and microfluidics. She has been AIAA associate fellow since 2000.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Heat transfer deterioration in a supercritical water channel Min-Tsung Kao, Min Lee ∗ , Yuh-Ming Ferng, Ching-Chang Chieng Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30043, Taiwan
a r t i c l e
i n f o
Article history: Received 3 February 2010 Received in revised form 12 June 2010 Accepted 21 June 2010
a b s t r a c t Supercritical water is the working fluid in the supercritical water reactor (SCWR) because of its high thermal efficiency and simplicity. Computational fluid dynamics (CFD) technology has been applied in the studies of supercritical water in circular channels by solving conservation equations of mass, momentum, and energy. Both the renormalization group k-(RNG k-) and Reynolds stress equation model (RSM) turbulence models were applied with enhanced wall treatment (EWT) for Yamagata’s heat transfer enhancement (HTE) experiments. Reynolds Stress turbulence model (RSM) with the enhanced wall treatment (EWT) was used for diagnosis and comparison of the heat transfer deterioration (HTD) phenomena observed in the Shitsman’s experiments. The simulations confirmed the heat transfer deterioration (HTD) phenomenon and predicted the associated peak wall temperature and minimum heat transfer coefficient consistent with Shitsman’s experiment. Series simulations with various operational pressures and inlet temperatures (Tin ) indicated that the increases of both inlet temperature and operational pressure were very effective to relax the heat transfer deterioration. The inclusion of buoyancy effect in the physical model revealed that the buoyancy effect played role on the dramatic increase of the wall temperature, which indicated the important role of buoyancy force on HTD by limiting the convection and turbulence. Dimensionless parameter of Prandtl number, the ratio of momentum and energy diffusion, which changing dramatically near the wall with wide range from 0.8 to 16.6, led to very different patterns of momentum and energy transports in the small region and was another important parameter for the formation of HTD. This study concluded the important roles of buoyancy effect and Prandtl number on heat transfer deterioration of supercritical water inside circular tubes. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Supercritical water reactor (SCWR) is a potential candidate of the Gen IV systems because of its high thermal efficiency (45%) and highly simplified plant systems. The major concern using supercritical water as work fluid is the heat transfer characteristics due to large variations of thermal properties of supercritical water near pseudo-critical line (Fig. 1). It is well known that deterioration in heat transfer for supercritical fluid flowing vertically upward in a tube occurs at a high heat flux. The criterion of the onset of heat transfer deterioration for gas flow in the small diameter tube has been examined in the experimental data [1–4] and suggested an acceleration parameter Kv measuring laminarization and a Buoyance parameter Bo* determining the onset of buoyancy influence. Lee et al. [5] collected experimental data for nitrogen, helium and carbon dioxide and updated the traditional thresholds of the deteriorated turbulent heat transfer (DTHT) regimes in circular tube.
∗ Corresponding author. Tel.: +886 3 572 917; fax: +886 3 572 0724. E-mail address: [email protected] (M. Lee). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.06.028
Since the dependence of thermo-physical properties between the gas and supercritical fluid is very different, it is not appropriate to apply the criteria from gas flow to supercritical water. Shiralkar and Griffith [6] determined both theoretically (for supercritical water) and experimentally (for supercritical carbon dioxide) the limits of maximum heat flux for a particular mass flux and found that the heat transfer deterioration (HTD) occurred when the bulk fluid temperature was below and the wall temperature above the pseudo-critical temperature. A series of overview of the existing criteria have been presented by Pioro and Duffey [7], Cheng and Schulenberg [8], Anglart [9] and indicated the large differences. A number of review papers on supercritical water studies in 1970s and 1980s [10–15] had been reported including numerical analysis as well as experimental works and empirical correlations. Some of the experiments observed no heat transfer deterioration [16,17] but Shitsmann [13], Ornatskij et al. [15] and Yamagata et al. [12] did. In the literatures, there are several explanations and debates for the mechanism of heat transfer deterioration. They indicated that HTD can be caused by rapid variation of thermophysical properties, acceleration, buoyancy effect or combination of these phenomena [1,2,18]. Palko and Anglart [19] had studied
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Nomenclature Cp [KJ/kg K] fluid specific heat G [kg/m2 s] mass flux I [%] turbulent intensity P [MPa] operating pressures Pr [–] Prandtl number q [kW/m2 ] wall heat flux r [m] radial direction in cylindrical coordinates T [K] fluid temperature TC [K] temperature at central axis T −T T* [–] dimensionless temperature T ∗ = q / CpC u i
i i
u [m/s] velocity u* [–] dimensionless velocity, u/ui z [m] axial direction in cylindrical coordinates ˛ [m2 /s] thermal diffusivity [m2 /s] momentum diffusivity [kg/m3 ] density Subscripts C central axis i inlet condition
the influence of buoyancy and thermo-physical properties variations on heat transfer to supercritical water. They found that the influence of buoyancy forces was significant at low mass flow rates to create HTD. However, the designated mass flow for SCWR is high enough to neglect the buoyancy force. At high mass flow rates, a low-conducting layer close to the heated wall was created due to the variation of thermal conductivity and this layer acted as a thermal barrier causing the onset of HTD. Thus, heat transfer of supercritical water using CFD analysis has been of interest to analyze and to understand physical mechanism. The main difficulties in numerical analysis are: (1) the choice of turbulence model, (2) buoyancy effect and acceleration effect due to the large variation of thermal properties, (3) the significant change of Prandtl number at pseudo-critical condition. Most of CFD analyses were successful on the study of heat transfer enhancement for supercritical water near pseudo-critical line and the computation experiences can be extended to study heat transfer deterioration. Kim et al. [10] used all the first order of turbulence models and six low-Reynolds turbulence models to study the heat transfer enhancement phenomenon and compared the results with Yamagata et al.’s experiment. He had a big success in using the renormalized group (RNG) turbulence model with
Fig. 1. Thermal properties of supercritical water at 23.3 MPa.
Fig. 2. Schematic diagram of solution domain and the applied boundary conditions: (a) Yamagata’s HTE and (b) Shitsman’s HTD experiments.
enhanced wall treatment (EWT) to predict Yamagata et al.’s experiment data. Nevertheless, in complicated geometry, like the rod bundle in reactor, first order of turbulence model cannot predict the secondary flow very well. Roelofs [14] used the second order turbulence model, Reynolds stress model (RSM) with EWT and also studied the heat transfer of supercritical water in Yamagata et al.’s experiment. He found RSM turbulence can predict the experimental data well than RNG did. Roelofs also discussed the effect of y+ value of first layer grid near the wall when simulating heat transfer of supercritical water and he suggested that y+ should be lower than 1. Furthermore, Roelofs predicted the mass flux and the corresponding heat flux for an onset of heat transfer deterioration without detailed descriptions of the phenomenon. Present study will study heat transfer deterioration in terms of the associated wall peak temperature and heat transfer coefficients using CFD analysis and compare with Shitsman’s experiment [13] to identify the physical phenomenon of heat transfer deterioration (HTD) for supercritical water and the effects by inlet temperature and operational pressure as well as the formation of HTD. In additional, the progress of HTD is illustrated by dimensional parameters for the progress of HTD and the recovering of heat transfer. 2. Physical and numerical model In the present paper, simulations are conducted for both heat transfer enhancement and deteriorations. The simulations for heat transfer enhancement not only provide the comparison against Yamagata’s HTE experiment but also the applicability of the computer code to both HTE and HTD problems. Yamagata et al. [12] studied heat transfer phenomenon (both HTE and HTD) as supercritical water flows in circular tube (diameter = 7.5 mm) with a range of parameters: operation pressure from 226 to 294 bar, applied heat flux (q ) from 116 to 930 kW/m2 and mass flux (G) from 310 to 1830 kg/m2 s. Present study chose the case of supercritical water flowing upward with q = 233 kW/m2 and G = 1260 kg/m2 s as the benchmark data for the simulations. Fig. 2(a) illustrates the schematic diagram of solution domain for Yamagata’s Experiment. Shitsman [13] studied the heat transfer deterioration phenomenon of supercritical water through circular pipe flow with five different heat fluxes applied on pipe wall. In the present study, the benchmark data for HTD is chosen from the cases of circular channels with radius 0.4 cm. The channel consists of 3 sections: unheated–heated–unheated sections at 0.6–2.9–0.4 m (Fig. 2(b)).
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Fig. 3. The mesh configuration for simulating (a) HTE and (b) HTD.
The experimental conditions undergoing heat transfer deterioration are with the mass flow rates of 430 kg/m2 , inlet temperature at 597.4 K, at operation pressure of 23.3 MPa, with wall heat flux of 386.134 kW/m2 applied on heated section and at Reynolds number ranging from 4.38 × 104 to 8.6 × 104 . The properties near pseudocritical conditions are varied sharply for supercritical water. The simulations are performed using thermal properties table from the National Institute of Standards and Technology (NIST) Chemistry webbook [20]. Non-slip and constant heat flux are the boundary conditions on wall for both HTE and HTD simulations. 2.1. Governing equations and turbulence model In this study, distributions of flow, temperature fields, and turbulent intensity as well as Prandtl number in the computational domain were obtained by solving the equation of continuity, energy, and momentum with Reynolds stress turbulence model
Fig. 5. Computed (a) wall temperature (b) heat transfer coefficient compared with Shitsman’s experiment at Tin = 597.4 K, P = 23.3 MPa.
(RSM) or renormalization group k-(RNG k-) [21]. RSM, known as second-moment closure model, closes the Reynolds-averaged Navier–Stokes equations by solving additional transport equations for the Reynolds stresses. The isotropic eddy viscosity assumption used in standard k- equation [21] is removed by using RSM. RSM can account for the effects due to streamline curvature, swirl, rotation, high strain rates, and secondary flow in ducts. Enhanced wall treatment is applied on near-wall region, which is a near-wall modelling approach that combines a two-layer model with enhanced wall functions. The near-wall mesh is fine enough to be able to resolve the laminar sublayer with first node of y+ near 1, then the enhanced wall treatment is identical to the traditional two-layer zone method. 2.2. Grid generation The thermal properties of supercritical water, like density, specific heat, viscosity and thermal conductivity, vary dramatically as approaching to the pseudo-critical conditions. Thus, very fine mesh is required to resolve the heat transfer phenomenon at nearwall region at temperature near the critical point. Furthermore, the application of enhanced wall treatment needs very fine grid near wall (y+ ∼ 1).
Fig. 4. Heat transfer coefficient versus bulk temperature.
2.2.1. Computational grid for Yamagata’s HTE experiment Fig. 3(a) shows the schematic diagrams of the computational meshes with 30 grids in r direction with successive ratio of 1.2. The y+ ranges from 1.2 to 2.5 at first grid near the wall for solving Yamagata’s HTE Experiment. Grid independence tests were conducted with different node numbers in the axial direction, i.e. node numbers were 20, 30, and 40 with the total node numbers of 55,000, 82,500 and 110,000, respectively. Less than 1% difference was observed between the grids of 82,500 and 110,000 nodes.
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Fig. 6. 15 Simulation results compared with Shitsman’s experiment at Tin = 597.4 K (a), (c) and (e) wall temperature and (b), (d) and (f) heat transfer coefficient.
2.2.2. Computational grid for Shitsman’s HTD experiment Fig. 3(b) shows that a 30 uniform prism layer is generated at distance 0.0075 cm from wall (i.e. radial position ranging from 0.3925 to 0.4 cm) and 60 grids are generated in region of radius less than 0.3925 cm with successive ratio of 1.08. The total mesh size is 540,000 with y+ ranging from 0.2 to 0.925 at first grid near the wall. Since the temperature gradient near the heated wall for the HTD case is sharper than that for the HTD case, much more grids were applied near heated wall region to avoid the grid dependence (i.e. 30 more nodes at the first node compared in HTE case). 3. Results The simulations are conducted for both heat transfer enhancement and deteriorations and are compared with experiments. The results are discussed in the following sections.
3.1. Yamagata’s HTE simulation The heat transfer enhancement is caused by the sharp increase of specific heat near the pseudo-critical temperature [22]. Good predictions on heat transfer coefficient versus bulk temperature (Tb ) are obtained using both turbulence models as shown in Fig. 4, except the slightly over-estimation of heat transfer coefficient and the shifted maxima near the pseudo-critical temperature (656.2 K). The maximum heat transfer coefficient is observed at Tb ∼ 655.4 K instead of at the pseudo-critical temperature (656.2 K) where the peak value of specific heat is occurred. The good prediction of HTE implies the capability of computations using Computer Software FLUENT and the adequacy of the grid system applied for supercritical fluid in circular channels.
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3.2. Shitsman’s HTD simulation Fig. 5 (a) and (b) plot the computed wall temperature and the heat transfer coefficient (h) versus weighted enthalpy at the cutting plane z, respectively. Since the enthalpy increases from inlet as heat flux applied in the heated section, the enthalpy has been chosen to replace the length along the Z direction and illustrated the results in the literatures. The observation confirms the heat transfer deterioration (HTD) phenomenon and captured the major physics. Nevertheless some discrepancies between the computed and measured wall temperature and heat transfer coefficient are shown. Considering uncertainty in measurements and the corresponding deviations in thermal properties at operation conditions, a set of additional 14 simulations have been conducted at different operation pressures and inlet temperatures. The operation conditions include five different operation pressures, 22.8, 23, 23.3, 23.4 and 23.9 MPa and 3 different inlet temperatures, 590, 597.4 and 603 K. 3.2.1. Effect of operational pressure on HTD With the same inlet temperature 590 K, Fig. 6 (a) and (b) shows the wall temperature variations and heat transfer coefficient along the flow direction at operating pressures (P) ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 859.8, 869, 877.8, 810.4, 765.9 K at operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 1.66, 1.59, 1.53, 2.15, and 2.96 kW/m2 K, respectively. It indicates the peak wall temperature of 877.8 K and a minimum heat transfer coefficient (HTD) of 1.53 kW/m2 K are occurred at bulk enthalpy of 1668 KJ/kg at P = 23.3 MPa for inlet temperature 590 K. As the inlet temperature is increased to 597.4 K, Fig. 6(c) and (d) shows the wall temperature variations and heat transfer coefficients along the flow direction at operating pressures ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 843.9, 862.1, 864.9, 792.9, 719.4 K at operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 1.81, 1.65, 1.63, 2.42, and 4.49 kW/m2 K, respectively. It indicates that the peak wall temperature of 864.9 K and a minimum heat transfer coefficient of 1.63 kW/m2 K are occurred at bulk enthalpy of 1685 KJ/kg at P = 23.3 MPa for inlet temperature 597.4 K. As the inlet temperature is further increased to 613 K, Fig. 6(e) and (f) shows the wall temperature variations and heat transfer coefficient along the flow direction at operating pressures ranging from 22.8 to 23.9 MPa, respectively. The peak wall temperatures are 709.0, 753.4, 776.1, 704.6, and 704.9 K for operation pressures 22.8, 23.0, 23.3, 23.4, and 23.9 MPa, respectively. The minimum heat transfer coefficients are 4.86, 3.35, 2.79, 5.08, and 5.10 kW/m2 K, respectively. It indicates that the peak wall temperature of 776.1 K and a minimum heat transfer coefficient of 2.79 kW/m2 K are occurred at bulk enthalpy of 1768 KJ/kg at P = 23.3 MPa for inlet temperature 613 K. Table 1 summarizes the minimum heat transfer coefficients, peak wall temperature for the series of the predictions at different operation pressures and inlet temperatures. The worst condition occurs at operation pressure of 23.3 MPa and temperature of 590 K, comparing the experimental conditions at 23.3 MPa and 597.4 K by Shitsmann. For inlet temperature of 597.4 K, Table 1 indicates that the most severe heat transfer deterioration occurs at P = 23.3 MPa with the minimum heat transfer coefficient of 1.63 kW/m2 K. Similar trend o is observed at Tin = 613 K. If operation pressure is raised from 23.3 to 23.4 MPa, the peak wall temperature is lowered from 877.8 to 810.4 K (67.4 degree, ∼7.7%), from 864.9 to 792.9 K (72 degree, ∼8.3%) and from 776.1 to 704.6 K (71.5 degree, ∼9.2%) for Tin = 590, 597.4 and 613 K respectively. It indicates that the
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Table 1 Predicted peak wall temperature (K) and minimum heat transfer coefficient h (kW/m2 K) for each simulation. Peak wall temperature and minimum heat transfer coefficient of each simulation case (peak wall temperature (K). Minimum heat transfer coefficient (kW/m2 K)) Operation P (MPa) Tin (K)
22.8 23.0 23.3 23.4 23.9
590
597.4
613
(859.8, 1.66) (869.0, 1.59) (877.8, 1.53) (810.4, 2.15) (765.9, 2.96)
(843.9, 1.81) (862.1, 1.65) (864.9, 1.63) (792.9, 2.42) (719.4, 4.49)
(709.0, 4.86) (753.4, 3.35) (776.1, 2.79) (704.6, 5.08) (704.9, 5.10)
operation pressure play an important role in heat transfer deterioration phenomenon at around 23.3 MPa. HTD is not observed at P = 23.4 MPa with Tin = 613 K (Fig. 6(e) and (f)). As the operation pressure is raised from 23.4 to 23.9 MPa at Tin = 590 K, the peak wall temperature decreases from 810.4 to 765.9 K (Fig. 6(a)), i.e. 5.5% change of the peak wall temperature with Tin = 590 K. Overall speaking, alleviation of heat transfer deterioration is observed for operation pressure higher than or equal to 23.4 MPa or inlet temperature as high as 613 K. 3.2.2. Effects of inlet temperature on HTD For operating pressure at 22.8 MPa, minimum heat transfer coefficient is recovered (or HTD is diminished) as the inlet temperature is increased from 590 to 613 K as comparing Fig. 5(a), (c) and (e). Similar observations are shown for the supercritical water operates at 23.0, 23.4 and 23.9 MPa also. For inlet temperature as high as 613 K, heat transfer deterioration is disappeared for all pressures except for 23.0 and 23.3 MPa (Fig. 6(e)). 3.2.3. Effect of buoyancy force on HTD Fig. 7 shows the simulation results of wall temperature with and without considering the effect of buoyancy force (gravity) under P = 23.3 MPa and Tin = 590 K. If the buoyancy effect is not taken into account, the wall temperature increases slowly along Z direction. However, as the buoyancy effect is considered in the simulation, wall temperature experiences a rapid rise and reaches a peak of wall temperature (877.8 K) at Z = 114.65 cm. It implies that the pseudocritical condition (651.75 K for P = 23.3 MPa) occurs at Z = 114.65 cm and r/R = 0.9 with fluid temperature at 626 K. This indicates that buoyancy effect plays an important role in heat transfer deterioration, which is very different from that in heat transfer enhancement [19].
Fig. 7. Wall temperature variation with/without Buoyancy effect considered on HTD.
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Fig. 8. Dimensionless parameters at section levels before and after HTD.
3.2.4. Discussion of HTD progress by dimensionless parameters The unheated section of the circular tube from Z = 0 to 60 cm allows supercritical water flow to be fully developed. With wall heat flux of 386.134 kW/m2 applied from Z = 60 to 350 cm, the supercritical water is heated with a sharp rise before it reaches the maximum temperature at Z = 114.65 cm (Fig. 7). Heat transfer deterioration is not severe at the section of Z = 70–100 cm but the apparent HTD is observed at Z = 105–130 cm. Heat transfer recovers and HTD diminishes after Z = 130 cm. Fig. 7 illustrates the wall temperature variations before, during, and after HTD. Wall temperature and heat transfer coefficients are related to the temperature gradient, velocity gradient, turbulent intensity, and the Prandtl number distribution near the wall. In this paper, the discussion of HTD progress will be based on two lines; (1) based against Prandtl number profile at individual Z-sections: correlating these profiles at chosen sections of Z = 90, 110, 114.65, 120 and 130 cm, and (2)
based on the increased of Z: illustrating the progress of the profiles of Prandtl numbers, mass flux, and turbulent intensity as flow approaching and leaving HTD (i.e. as Z increases). The distributions of non-dimensional parameters of temperature (T*), velocity (u*), turbulent intensity (I) against Prandtl number (Pr) at sections of Z = 90, 110, 114.65, 120 and 130 cm are shown in Fig. 8(a)–(e). These are the representative profiles showing the HTD progress in regions before HTD (e.g. Z = 90 cm), approaching HTD (e.g. Z = 110 cm), during HTD (e.g. Z = 114.65 cm) and after HTD (e.g. Z = 130 cm). At Z = 70 cm, Prandtl number (Pr) is nearly constant (0.8) except for a rise at very near-wall region (r/R > 0.99375), a moderate temperature gradient (T* ∼ 367), a relatively thick boundary layer, and a turbulent intensity level of ∼4% with a peak located at r/R ∼ 0.9875 are observed. At Z = 90 cm, the region of high Pr is expanded to a sharp peak, wall temperature (T* ∼ 560) with a sharp temperature decrease away from the wall
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Fig. 9. Progress of Prandtl number profiles (a) before and (b) after HTD. Fig. 11. Mass flux for P = 23.3 MPa, Tin = 590 K (a) r/R = 0–1 and (b) r/R = 0.975–1.
Fig. 10. Turbulent intensity I (%) for P = 23.3 MPa, Tin = 590 K (a) r/R = 0–1 and (b) r/R = 0.875–1.
is appearing, a wall peak of turbulent intensity (∼4%) exists, and a smooth velocity profile is observed. At Z = 110 cm where the HTD approaching with wider Prandtl number peak, wall temperature rise (T* ∼ 900), higher velocity, and a sharper wall peak of turbulent intensity with magnitude decrease (∼3%) are observed. As flow near HTD (Z = 114.65 cm), Prandtl number peak is wider and moves farther from wall, higher wall temperature (T* ∼ 1600), and lower turbulence intensity (∼2%) of narrower wall peak are correlated. As heat transfer recovered from HTD at Z = 120 cm, the Prandtl number profiles moves toward wall again, thinner velocity boundary layer, lower wall temperature (Tw * ∼ 760), and higher turbulence intensity wall peaks are recovered (∼4%). As flow leaving HTD with narrower Prandtl number peak, all these flow and temperature profiles are recovered. As the flow goes downstream, the peak of Prandtl number is moved away from the wall to where the largest velocity occurred and this is where the worst heat transfer happened (i.e. highest wall temperature and lowest heat transfer coefficient at Z = 114.65 cm) and then the higher momentum at very near-wall region can be transported out to speed up the whole fluid region and heat transfer becomes better. In all the simulation cases, Prandtl number ranges from 0.8 to 16.6. Since Prandtl number is the ratio of momentum and energy diffusion, the fluid region with Prandtl number much larger than 1 indicates the fluid experiencing much better momentum diffusion than energy diffusion and much thicker hydraulic boundary layer than thermal boundary layer as Fig. 9 shows. As the flow approaching the pseudo-critical point (Z = 110 cm), high Pr region is extended to r/R ∼ 0.9625 with peak located r/R ∼ 0.9925, turbulent intensity is reduced to 2–3% level (which is equivalent to laminarization as observed by previous studies (1–4)). Fig. 9(a) plots the progress of Prandtl number profiles before HTD, the regions of Prandtl number peak are increased as Z increases, the peaks are not only wider and higher but also moved away from the wall as flow approaching HTD.
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Fig. 10 plots the progress of turbulent intensity profile before and after HTD, the turbulent intensity decreases as approaching HTD and recovers after HTD, which implies the laminarization. The laminarization is also revealed by the profiles of mass flux near the wall (Fig. 11). Mass flux near wall decreases as flow approaching HTD and recovers after HTD. The decreasing of turbulent intensity deteriorates the heat transfer. At the sections near HTD, heat is accumulated at the fluid region between the heated wall and the peak of Prandtl number, thus the temperature difference T at this region increases. Larger temperature difference induces larger buoyancy force at very near-wall region. The buoyancy force increases the velocity and changes the velocity profile with smaller velocity gradient and smaller turbulent intensities at very near-wall region. (Fig. 10(a) and (b)). 4. Conclusions Heat transfer deterioration in supercritical water channel is studied by solving conservation laws of mass, momentum, and energy with Reynolds Stress turbulence model and enhanced wall treatment using CFD technology. The simulations confirm that the buoyancy effect in addition to laminarization play an important role resulting from large variations of thermal properties, which is very different from that in heat transfer enhancement. The simulation results confirmed the heat transfer deterioration phenomenon and captured the major physics although the location and magnitude of peak wall temperature were not perfectly predicted as compared with the Shitsman’s experiment data under the same operation condition. 15 simulations with 5 operational pressures and 3 inlet temperatures (Tin ) have been conducted and indicated that the increases of both inlet temperature and/or operational pressure were very effective to relax or relieve the heat transfer deterioration. Prandtl number is introduced and identified as a representing parameter of physical property to describe the progress of HTD. The enlarging region of high Prandtl number ranging from 0.8 to 16.6 as approaching HTD implies the high ratio of momentum diffusion compared to energy transport and thus the laminarization of turbulence. HTD is formed because the buoyancy force is confined at very near-wall region at the beginning of heating. This study concluded the important roles of buoyancy effect and Prandtl number on heat transfer deterioration of supercritical water inside circular tubes. Acknowledgement The authors highly appreciate the supports from the National Science Council, Taiwan under contract NSC98-3114-E-007-007. References McEligot, D.M., Coon, C.W., Perkins, H.C., 1970. Relaminarization in tubes. Int. J. Heat Mass Transfer 9, 1151–1152. Bankston, C.A., McEligot, D.M., 1970. Turbulent and laminar heat transfer to gases with varying properties in the entry region of circular ducts”. Int. J. Heat Mass Transfer 13, 319–344. Moretti, P.M., Kays, W.M., 1965. Heat transfer to a turbulent boundary layer with varying free-stream velocity and varying surface temperature—an experimental study. Int. J. Heat Mass Transfer 8, 1187–1202.
McEligot, D.M., Jackson, J.D., 2004. Deterioration criteria for convective heat transfer in gas flow through non-circular ducts. Nucl. Eng. Des. 232, 327–333. Lee, J.I., Hejzlar, P., Saha, P., Stahle, P., Kazimi, M.S., McEligot, D.M., 2008. Deteriorated turbulent heat transfer (DTHT) of gas up-flow in a circular tube: experimental data. Heat Mass Transfer 51, 3259–3266. Shiralkar, B.S., Griffith, P., 1970. The effect of swirl, inlet conditions, flow direction, and tube diameter on the heat transfer to fluids at supercritical pressure. J. Heat Transfer Trans. ASME 92 ((3) August), 465–474. Pioro, I.L., Duffey, R.B., 2005. Experimental heat transfer in supercritical water flowing inside channels (survey). Nucl. Eng. Des. 235, 2407–2430. Cheng. X., Schulenberg, T., 2001. Heat transfer at supercritical pressures—literature review and application to a HPLWR. Scientific Report FZKA6609, Forschungszentrum Karlsruhe. Anglart, H., 2009. Heat transfer deterioration in application to the HPLWR mechanisms identification and ranking table. In: Proceedings of the Fourth International Symposium on Supercritical Water Cooled Ractors, Heidelberg, Germany, March 8–11. Kim., S.H., Kim, Y.I., Bae, Y.Y., Cho, B.H., 2004. Numerical simulation of the vertical upward flow of water in a heated tube at supercritical pressure. In: Proceedings of ICAPP. Cheng, X., Kuang, B., Yang, Y.H., 2007. Numerical analysis of heat transfer in supercritical water cooled flow channels. Nucl. Eng. Des.. Yamagata, K., Nishikawa, K., Hasegawa, S., 1972. Forced convection heat transfer to supercritical water flowing in tubes. Int. J. Heat Mass Transfer 15, 2575–2593. Shitsman, M.E., 1963. Impairment of the heat transmission at supercritical pressures. High Temp. 1 (2), 237–244. Roelofs, F., 2004. CFD Analyses of heat transfer to supercritical water flowing vertically upward in a tube. Under the contract of the Netherlands Ministry of Economic Affairs. Ornatskij, A:P., Glushchenko, L.F., Kalachev, S.I., 1971. Heat transfer with rising and falling flows of water in tubes of small diameter at supercritical pressures. Thermal Engineering 18 (5), 137–141. Dickinson, N.L., Weich, C.P., 1958. Heat transfer to supercritical water. ASME 80, 745–751. Domin, G., 1963. Wärmeübergang in kritischen und überkritischen Bereichen von Wasser in Rohren. BWK 15 ((11) November). Mikielewicz, D.P., Shehata, A.M., Jackson, J.D., McEligot, D.M., 2002. Temperature, velocity and mean turbulence structure in strongly-heated internal gas flows—comparison of numerical predictions with data. Int. J. Heat Mass Transfer 45, 4333–4352. Palko, David, Anglart, Henryk, 2008. Numerical study of the influence of buoyancy and thermo-physical properties variations on heat transfer to supercritical water. In: The Seventh International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety Seoul, Korea, October 5–9. http://webbook.nist.gov/chemistry/fluid/. FLUENT 6.3 User’s guide. Renz, F.U., Bellinghausen, R., 1986. Heat Transfer in a vertical pipe at supercritical pressure. In: Eighth International Heat Transfer Conference, vol. 3, pp. 957–962. Mr. Min-Tsung Kao received his B.S. and M.S. degrees from the Department of Engineering and System Science of National Tsing Hua University (NTHU) of Taiwan at 2007 and 2009, respectively. He is serving his military duty for the country now. Prof. Min Lee received his B.S. and M.S. degrees in Nuclear Engineering from NTHU. He received his Ph.D. degree in Nuclear Engineering from Massachusetts Institute of Technology in 1985. Before he went back to NTHU and became a professor at Department of Nuclear Engineering in 1989, he had worked at Brookhaven National Laboratories for 3 and half years. His expertise includes thermal hydraulic analysis of nuclear power system, probabilistic safety assessment of nuclear Power Plant, and heat transfer. Prof. Yuh-Ming Ferng received his B.S. and Ph.D. degrees in Nuclear Engineering Department from NTHU at 1986 and 1990, respectively. Before he joined the Department of Engineering and System Science at 2008, he worked at Institute of Nuclear Energy Research of Atomic Energy Commission of Taiwan. His expertise includes computational fluid dynamics, turbulent flow, and CFD simulations of reactor components. Prof. Ching-Chang Chieng received her B.S. degree in Nuclear Engineering from National Tsing Hua University, Hsinchu, Taiwan, then she completed her M.S. degree in Chemical Engineering from University of Rhode Island, U.S.A. and Ph.D. in Aerospace and Ocean Engineering from Virginia Polytechnic Institute and State University, U.S.A. She joined Department of Engineering and System Science, National Tsing Hua University as a professor in 1981. Her expertise includes computational fluid dynamics, turbulent flow, and microfluidics. She has been AIAA associate fellow since 2000.