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Critical heat flux experiments and a post-CHF heat transfer analysis using 2D inverse heat transfer
Nuclear Engineering and Design 337 (2018) 17–26
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Critical heat flux experiments and a post-CHF heat transfer analysis using 2D inverse heat transfer☆
T
⁎
Juliana P. Duartea, , Dawei Zhaob, Hangjin Joa, Michael L. Corradinia a b
Engineering Physics Department, University of Wisconsin, 1500 Engineering Drive, Madison, WI 53703, United States CCNC Key Laboratory on Nuclear Reactor Thermal Hydraulics Technology, Nuclear Power Institute of China, Chengdu 610213, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Critical heat flux (CHF) Departure from nucleate boiling (DNB) Dryout Small modular reactor Inverse heat transfer
The critical heat flux (CHF) is one of the main thermal-hydraulics safety limits in water-cooled reactors. At CHF, a film of vapor is formed on the heated wall and the wall temperature can sharply increase in a short period of time, which may lead to damage of the heater surface. In spite of many studies, the CHF mechanisms are still not well understood due to the complexity of this two-phase phenomenon and its dependence on local thermalhydraulic conditions. Two-phase boiling experiments have been conducted to observe CHF and post-CHF behavior in prototypical conditions for small modular reactors (mass flux: 560–1570 kg/m2.s, pressure: 7.6–16.4 MPa, inlet subcooling: 160–440 kJ/kg) in a 2 × 2 square rod bundle geometry with a chopped-cosine power profile at the University of Wisconsin-Madison. The fuel rods temperature history during and following CHF were used in the solution of the two-dimension inverse heat transfer problem to estimate the wall temperatures and wall heat fluxes. This analysis showed different transient boiling curves for different flow regimes that differ qualitatively and quantitatively from the typical boiling curve considered in steady-state two-phase heat transfer analysis. The experiments suggest that the inverse heat transfer analysis approach can be used to estimate the post-CHF heat transfer and to better understand the CHF mechanisms at high pressure typical of water-cooled reactors.
1. Introduction The ability to transfer heat with a minimal temperature difference is a limiting factor in heat transport systems that operate at high heat fluxes. In many industrial applications, such as power plant technologies, the heat transport systems operate with two-phase vapor-liquid flows to optimize heat transfer and minimize temperature differences. The knowledge of the heat transfer mechanisms in different two-phase flow regimes is important to define safety margins during normal and abnormal operational conditions. In these two-phase heat transport systems, such as exist in the reactor core of light water reactors (LWR), the maximum operating power is restricted to a maximum heat flux between the liquid and the heated surface. This limiting condition is known as the critical heat flux (CHF) phenomenon. At CHF, a film of vapor is formed on the heated wall and the wall temperature can sharply increase in a short period of time, which may lead to damage of the nuclear fuel rods. This phenomenon is also characterized by more mechanistic terminology known as film dryout or departure from nucleate boiling (DNB). The former term refers mostly to conditions found in boiling water reactors (BWR), where the ☆ ⁎
fuel rod surface is completed dried out downstream of the CHF point without an annular liquid film present. The latter term refers to conditions found in pressurized water reactors (PWR), where vapor bubbles accumulate near the heated wall and coalesce into a film of vapor, thereby leading to a localized increase in the heater wall temperature. The difference between the DNB and dryout is discussed by Kitto (1980) as a limiting quality phenomenon. The DNB occurs at lower quality levels while dryout occurs at higher qualities. Kitto (1980) defines a limiting quality region in which there is a considerable change in the critical heat flux for a small change in quality. The critical heat flux is predicted in thermal-hydraulic computational codes, such as TRACE (USNRC, 2013), and CTF (Salko and Avramova, 2015), by correlations from data gathered in either BWR or PWR conditions. One exception is the look up table 2006 (Groeneveld et al., 2007) that covers critical heat flux data in a large range and presents a limiting quality region. However, the thermal-hydraulic codes fail to relate the flow regime to the critical heat flux mechanisms. As shown in this paper and stated in Groeneveld et al. (2007), void fractions in the annular flow regime exist below the limiting quality. In fact, the annular flow above the limiting quality is defined by a very thin liquid film (Groeneveld et al., 2007)
A brief version of this paper was published in ANS winter meeting 2017 (Duarte et al., 2017). Corresponding author. E-mail addresses: [email protected] (J.P. Duarte), [email protected] (D. Zhao), [email protected] (H. Jo), [email protected] (M.L. Corradini).
https://doi.org/10.1016/j.nucengdes.2018.06.011 Received 15 January 2018; Received in revised form 6 June 2018; Accepted 7 June 2018 0029-5493/ © 2018 Elsevier B.V. All rights reserved.
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design is not typical of nuclear reactors but similar grid spacer designs have been used in related experimental studies (Xiong et al., 2015; Moon et al., 2005). The lateral walls are part of the flow channel and the inner walls are 0.79 mm thick. There are four grid spacers in the heated length with 12.70 mm height and two grids outside the heated length with 6.35 mm height. The power is shaped by a helical resistance filament made from Inconel 718 with a varying pitch to be close conformance with the axial profile (Eq. (1)). The filament is filled with BN which is also used as insulating sleeves between the filament and the sheath.
and the CHF mechanisms are not well understood despite of the many studies of critical heat flux (Carey, 2008). To understand the different mechanisms of vapor formation at different local qualities, new critical heat flux data were analyzed using two-dimensional inverse heat transfer. The CHF experiments were performed at the high pressure heat transfer facility built to study the heat transfer at light water small modular reactor conditions, i.e., low mass fluxes and moderate to high pressures (Greenwood et al., 2017). The flow channel was modified and new grid spacers were designed for the current work. A set of pre-CHF experiments in single-phase and two-phase flow were performed and compared to the subchannel code CTF in order to estimate the heat losses of the test section and the contact resistance of the thermocouples embed into the heater’s walls. A new set of CHF experiments are presented in this paper. The modifications have shown an improvement of the CHF prediction when compared to the look up table 2006 (Groeneveld et al., 2007).
x 1 ⎞ q (x ) = θ0 + θ1cos ⎛2·θ2 ⎛ − ⎞ ⎝ HL 2 ⎠ ⎠ ⎝
(1)
where
θ0 = 0.82, θ1 = 0.68, θ2 = 2.44
3. Pre-CHF heat transfer analysis 2. Experimental facility Steady-state experiments at different mass fluxes, pressures, inlet temperatures, and powers were performed in order to characterize the facility. The experiments were simulated using CTF (Salko and Avramova, 2015). CTF is a two-fluid computational code with three fluids fields equations (liquid, vapor, and liquid drops). It solves the energy, mass, and transversal and axial momentum equations in 1D (with capability to develop 2D and 3D models). It simulates each subchannel and each rod separately, as shown in Fig. 4, and connects each subchannel using crossflow correlations for turbulent flow. A total of seventy-eight axial nodes were used for the CTF channel. Table 2 summarizes the main model choices used in CTF simulations. The experimental range covers single-phase and two-phase flows under subcooled and saturation boiling regimes:
The High Pressure Heat Transfer Facility (HPHTF) was designed to study heat transfer under a variety of pressures in single-phase, twophase, and supercritical fluid flows (Greenwood et al., 2017). In this work, the facility was configured to examine two-phase flow conditions and critical heat flux under small modular reactor conditions. The facility (Fig. 1) consists in a test section (4) with a 2 × 2 rod bundle electrically heated and with a heated length of 2 m, a high pressure pump (1), a heat exchanger (5), an accumulator used to pressurize the system with argon gas (7), and two bypass valves (3, 6). The orifice flow meter (2) was calibrated to measure the inlet mass flow rate. Details of the loop can be found in Greenwood (2015) and Greenwood et al. (2017). The new test section flow channel and the spacer grids, which were modified for these experiments, are described in this section. The rod diameter, pitch, and power shape are comparable to typical small modular reactor designs, such as NuScale Power (2016). Each rod has ten thermocouples (TC) located in different angular and axial positions, and a cosine axial power profile. The thermocouples are located between a clad and a sheath, both made from Monel K500. The clad and sheath thickness are 0.38 mm and 0.89 mm, respectively, and the rod diameter is 9.5 mm. The inlet and outlet temperatures are measured with thermocouples Type K with 1/8 in OD located between rods #1 and #4, and the bulk temperatures are measured at six axial positions with nine Type K TC 1/16 in OD. Fig. 2 shows the TC locations with respect to the power shape and spacer grids locations, and Table 1 shows the rod and square flow channel dimensions. The new grid spacers (Fig. 3) were designed to provide support to the rods and minimally affect the flow, with no mixing vanes. This
Pressure: 7.8–16.0 MPa Mass flow: 520–2200 kg/m2.s Inlet temperature: 63–309 °C Power per rod: 1–91 kW. The calibration of the thermocouples was verified at zero power and high mass flux. At these conditions, it is expected that all thermocouples would indicate the same temperature. The thermocouples are ungrounded Type K (Ni-Cr, Ni-Al) and were purchased in different batches (inlet, outlet, bulk, and wall thermocouples). The manufacture temperature range of Type K TC is from 0 to 1250 °C with a tolerance of 1.1 °C or 0.4%, whichever is greater. The maximum deviation found was 0.9 °C for the temperature range 18–105 °C, which is within the tolerance limit. The maximum temperature of these experiments was
Fig. 1. Basic process flow diagram of the high pressure heat transfer facility (HPHTF) (Greenwood et al., 2017). 18
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Fig. 2. Chopped cosine profile, thermocouple, and spacer grid positions (right). Circumferential thermocouple locations (left). Table 1 Bundle geometry.
Table 2 CTF main model choices.
Parameter
Dimension (mm)
Parameter
Dimension (mm)
Square channel Material Thickness Width Total length Corner radius
SS316 1.98 29.92 2161.5 2.29
Rod Outer diameter Clad thickness Sheath thickness Pitch Rod-to-wall Heated length (HL)*
9.5 0.38 0.89 12.6 1.93 2000
Parameter
Model chosen
Rod friction Entrainment and deposition Mixing and void drift
λ = 0.204 Re−02 Original model Single-phase coefficients: Km = 1.4* (equilibrium distribution weighting factor in void drift model) β = 0.005 (constant turbulent mixing coefficient) Two-phase model: Beus (1969) θ = 5* (ratio between the maximum twophase turbulent mixing coefficient and the single-phase coefficient) IAPWS IF97 Radial, axial and azimuthal conduction No radiation is modeled (NRAD = 0) Off
* The heated length started 97 mm after the beginning of the square channel.
Fluid property tables Conduction model flag Number of radiation channels Flag for the Yamanouchi canister quench model (spray cooling after LOCA) Flag for the radiation heat transfer calculation Critical heat flux (CHF) Choice for nucleate boiling model DNB check option
Fig. 3. Grid spacer geometry (Duarte et al., 2017).
Off No correlation for steady state simulations Thom’s correlation Groeneveld look-up tables for steady state simulations
* Suggested values from CTF manual Revision 0 (Salko and Avramova, 2015).
̇ = Q− ̇ ṁ ·cp·(Tout−Tin) Qloss
(2)
where
Q̇ is the electrical power (kW) ṁ is the inlet mass flow (kg/s) cp is average specific heat (kJ/kg) Tout , Tin are the measured outlet and inlet temperatures (°C). The heat loss was estimated to be equal to 6% of the total power. The maximum source of uncertainties are the thermocouple calibration and the inlet mass flow calibration (Greenwood, 2015), which leads to about 2% of uncertainty by error propagation in the entahlpy rise in the fluid. The heat loss was used to estimate the local fluid conditions, i.e., the local quality and void fraction. Fig. 5 shows a schematic view of the rod thermocouples embedded between 0.38 mm clad and 0.89 mm sheath both made from Monel K500. The thermocouple diameter is 0.51 mm Inconel 600 sheaths and
Fig. 4. CTF subchannels.
limited by the maximum temperature that the loop could be kept without significant heat loss in the heat exchanger for thirty seconds. Forty-five single-phase experiments were used to estimate the heated loss of the test section defined as: 19
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of forty-three experiments is shown in Appendix A. The power limit of the facility is 100 kW per rod. The complete experimental range is: Mass flux: 560–1570 kg/m2.s Pressure: 7.6–16.4 MPa Inlet subcooling: 160–440 kJ/kg. The experimental procedure follows similar steps as in Greenwood et al. (2017). However, instead of allowing the pressure to change while searching for CHF, the inlet conditions (mass flow, temperature and pressure) are kept constant by continuous adjusting them at each power step. After the inlet conditions are set as desired for a power lower than the CHF, a steady state is achieved, and the power is increased by approximately 1 kW/rod, and for each step a new steady state condition is reached until the CHF is detected. The Labview program automatically reduces the power by a small fraction (∼5%) once the maximum TC measurement reaches a specified trip setpoint. This process continues automatically until the TCs indicate complete rewetting. Fig. 8 shows the normalized key parameters during an experimental critical heat flux run. The scale does not represent actual fractions, for example, after the power is decreased, the pressure only decreases about 0.5 MPa for an experiment at 8.0 MPa. The CHF conditions were defined as the average of one second before the CHF detection (data was collected with a frequency of 10 Hz). The average CHF (total power divided by the total heat transfer area) trends with mass flux, pressure, and inlet subcooling can be seen from Figs. 9 and 10. As it is expected for the range of these experiments, the CHF increases as the mass flux and subcooling increases, and it decreases with the pressure for this pressure range. The average heat fluxes at the CHF condition were compared to the Look Up Table (LUT2006) (Groeneveld et al., 2007), Fig. 11. The operational conditions were simulated using CTF with the bundle power continuously increased by 1 kW/min and compared to the LUT2006 until the DNBR (departure from nucleate boiling ratio) in one or more of the subchannels falls below one. At this point, the average heat flux was defined as the total power divided by the total heat transfer area. This is one method to compare CHF data as discussed in Tong and Tang (1997). The error between the data and LUT2006 is a normal distribution with average equal to 2%, standard deviation equal to 6%, and the root mean square equal to 6%. No trend was observed with the mass flux, inlet subcooling, or experimental run number. The error, however, ″ > qpred ″ ) to a non-conservative moves from a conservative zone (qexp ″ < qpred ″ ) as the pressure increases, Fig. 12. It is worth prediction (qexp noting that the data were collected in a range of low mass fluxes compared to most of the critical heat flux data in a rod bundle available in the literature. Greenwood et al. (2017) compare the first CHF data from the HPHT facility with EPRI database (Fighetti and Reddy, 1982) showing the limited number of rod bundle data available at high pressure and low mass flow conditions. As also discussed in Greenwood et al. (2017), this was one of main motivation to build the HPHT facility. This trend was not clearly seen before because of the lack of control of the experimental pressure in the previous experiments. Compared to the LUT2006, part of the new data range follows in the light grey region of Groeneveld et al. (2007) table, which means that the CHF prediction was calculated based on selected methods rather than experimental data.
Fig. 5. Schematic view of the rod thermocouples (left) and the thermal resistance model (right).
ungrounded junctions. The TC have MgO insulation except at the tips which are backfilled with BN insulation. The wall temperatures measured by the thermocouples were compared to CTF results taking into account a correction due to the conduction through the clad wall for seventy-six experiments. The difference between the measured and predicted temperatures was found to be independent of Reynolds and Prandtl numbers and to consistently increase with the local power. Therefore, a correction factor was developed as a function of the power for each thermocouple in order to model any contact resistance effect produced. The total thermal resistance is a combination of the thermocouple position with respect to the heater coil, the contact resistance between the TC and the clad, and the axial conduction through the clad wall (Duarte, 2017). After applying the correction factors, the corrected wall temperature is compared to Thom’s correlation (Thom et al., 1965) with an standard deviation of ± 5 °C, Fig. 6. For the nucleate boiling regime, Cheng and Fang (2014) and Thom et al. (1965) correlations were compared and the average difference between them were 3 °C with a standard deviation of 2 °C for this set of conditions. Thom’s correlation was chosen because its faster numerical convergence. The corrected wall temperatures are used in the inverse heat transfer analysis with an uncertainty of ± 5 °C. 4. Critical heat flux experiments Critical heat flux experiments were performed under two mass fluxes (770 and 1500 kg/m2.s), five pressure (8, 9, 12, 14, and 16 MPa), and three inlet subcoolings (200, 340 and 420 kJ/kg). Fig. 7 shows how the main experimental matrix is distributed in these conditions. Few data were collected outside the main data matrix; the complete data set
5. Post-CHF heat transfer At high pressure conditions in a bundle geometry, it is difficult to obtain visual information of critical heat flux experiments because of material limitations. The understanding of the phenomena is then build from the data we can collect and the interpretation of the results. The
Fig. 6. Comparison between predicted and measured wall temperature after applying the correction factors. 20
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Fig. 7. Main experimental data matrix.
Fig. 8. Key parameters during an experimental critical heat flux run.
Fig. 10. Critical heat flux vs. pressure for high mass flow (∼1500 kg/m2.s) at different inlet subcooling.
Fig. 9. Critical heat flux vs. pressure for low mass flow (∼770 kg/m2.s) at different inlet subcooling.
Fig. 11. Critical heat flux data compared to LUT2006.
temperature of the heater rods that determines the occurrence of CHF (by a sharp increase) is usually measured inside the heater cladding. At the CHF, the rod temperature increases because of the deterioration of the heat transfer from the wall to the liquid due to the vapor formation
or liquid film dryout. To calculate the wall temperature and the actual heat flux transfer to the liquid/vapor mixture, we need to solve the inverse heat transfer problem. The temperature increases and decreases after CHF was analyzed using an inverse heat transfer (IHT) computational model, INTEMP 21
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way, the TC measurements are used to compensate for the lack of information on the unknown boundary condition and the conduction problem can be solved. The IHT problem belong to the class of Ill-posed mathematical problems, in contradiction to the Well-posed problems in which all initial and boundary conditions are known (Ozisik and Orlande, 2000). A total of fifty axial nodes of 2.2 cm each and ten radial nodes were used from 0.9 m to the top of the heated length—only the top portion of the rod was simulated because of the location of the thermocouples. Adiabatic boundary conditions were used on the top and the bottom of the rod domain. A sensitivity analysis of the boundary conditions, mesh size, and also other numerical parameters were performed and found to be insignificant compared to other uncertainty sources (Duarte, 2017)—see Table A.2. The main source of uncertainty in the surface temperature is due to the correction factors, as discussed in Section 3, and it is estimated to be ± 5 °C. The IHT analysis calculates the surface temperature based on the two-dimensional transient conduction problem. The cladding properties are included in the solution as a temperature-depended table. A limitation of the IHT analysis is that only one boundary condition can be estimated for each temperature history and therefore, the (known and unknown) heat fluxes were discretized to seven boundary conditions which correspond to the seven axial temperature measurements. This limitation is inherent to this kind of experiment due to the limited number of thermocouples that can be placed in the rod during its fabrication. The local power error is estimated to be ± 5% according to the rod manufacturer (Stern Labs, 2012). The average heat flux used in the inverse heat transfer analysis does not differ more than 7% of the estimated local heat flux that follows the cosine shape profile, for the cases presented here. On the other hand, the 2D IHT accounts for axial conduction and provides us a better understanding of the post-CHF phenomenon as discussed in this section. For each CHF test, the temperature increase and decrease, after the power reduction, were recorded as shown in Fig. 14. The input heat flux (qin) was simulated as a known boundary condition applied at the inner sheath wall (Ri = 3.48 mm). The TC temperature data were used to calculate the wall temperature and the unknown boundary condition, i.e., the wall heat flux (qout in Fig. 14) (at = 4.75 mm).
Fig. 12. Error trend with pressure of the CHF data compared to LUT2006.
(TRUCOMP, 2003). The IHT method is a common engineering analysis approach that relies on temperature and/or heat flux measurements at a particular location for the estimation of unknown quantities, such as temperature or heat flux boundary conditions (BC), initial conditions (IC), or material properties (Ozisik and Orlande, 2000). INTEMP solves the two-dimensional nonlinear inverse heat conduction problem using the Crank-Nicolson or the Fully Implicit finite element formulation (TRUCOMP, 2003). In the particular case of this research work, the inverse problem can be understood in Fig. 13. The unknown figure to be quantified is the transferred heat flux from the rod surface to the working fluid that decreases after CHF causing the heater rod clad surface temperature to increase. Fig. 13 shows the “unknown heat fluxes”, i.e., the unknown boundary conditions on the right side, at the rod surface. The “known heat fluxes” represent the rod power applied on the sheath inner surface, i.e., the power divided by the heat transfer area. The thermocouples are shown by circles with the respective node number. In this
0.89 mm (Sheath) 0.38 mm (Clad)
TC groove BN insulaƟon Heater ribbon
INTEMP boundary condiƟons
Fig. 13. INTEMP mesh and rod domain. 22
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Fig. 16. Experimental heat transfer coefficients for Exp. #1 (NB – nucleate boiling, TB – transition boiling, FB – film boiling).
Fig. 14. Inverse heat transfer analysis for CHF for Exp. #1 (1521 kg/m2.s, 9.1 MPa, 209 kJ/kg).
The Exp. #1 is a representative example of the behavior observed for the experiments at low pressure and high local qualities. Its local equilibrium quality and void fraction are 0.20 and 0.75 (calculated by CTF at the CHF location), which means that, according to CHF flow regime map, this is a churn flow. The behavior of higher local void fraction experiments in the annular/mist flow regimes (α ≥ 0.8) is, in general, similar. For example, Fig. 17 shows the behavior of Exps. #11 and #35. These experiments were chosen because they were performed at the same pressure and mass flux and the CHF occurred at the same axial position (TC #5). The local qualities and void fractions are 0.29 and 0.83 for the Exp. #11, and 0.34 and 0.86 for Exp. #35. In fact, the maximum and minimum heat fluxes occurred at virtually the same wall temperatures and the heat transfer coefficient follows the same profile as shown in Fig. 16. Fig. 18 shows the effect of the mass flux on the transient boiling curve. Exp. #8 and #16 were chosen because in both cases the CHF occurred in the same axial position (TC#5). The local qualities and void fraction are 0.18 and 0.73 for Exp. #8, and 0.31 and 0.81 for Exp. #16. Notice that the difference between Exp.# 11 and #16 is the pressure, and the difference between the Exp. #8 and #1 is the inlet subcooling condition and the local quality. It was observed that the minimum heat flux point becomes unclear as the pressure increases and the wiggles in the heating path become more frequent as the local void fraction decreases.
Fig. 15. Heat flux versus wall temperature for Exp. #1 (1521 kg/m2.s, 9.1 MPa, 209 kJ/kg).
Note that for Exp. #1, after the CHF event, the heat flux leaving the wall significantly decreases, reaches a minimum, and starts to increase again before any power change is triggered by the control system. This behavior indicates the presence of degraded post-CHF heat transfer and passage through the minimum film boiling temperature from which a stable film boiling is formed on the wall. From this minimum point, the heat flux continuously increases with the increase of the wall temperature until the power is decreased in two steps of 5% and the wall is rewetted. Fig. 15 shows the wall heat flux versus the wall superheat temperature for the same conditions of Fig. 14. The circled points indicate the power steps at 29.5 and 31.5 s. The shape of Fig. 15, with heat fluxes higher than the CHF during the cooling of the heater wall, has been discussed before by Stosic (2005) in the analyze of Igushi et al. (2001)’s experiments. The hysteresis between the heating (bottom part of the curve) and the cooling (top part of the curve) can be explaining by solving the 1D transient coupled problem with the fluid thermal-hydraulic condition and the heat conduction in the solid material. Because Fig. 15 is a transient heat flux vs. ΔTwall curve, we will call it as a transient boiling curve. The conclusion that the minimum and maximum points in Fig. 15 represents the formation and collapse of a stable film of vapor near on the wall can also be drawn from Fig. 16. Fig. 16 shows the heat transfer ″ /(Twall−Tsat ) ] for the Exp. #1. The location of coefficient [HTC = qwall the maximum and minimum heat fluxes are indicated and one can noticed a small and nearly constant HTC between these two points.
Fig. 17. Effect of the inlet subcooling on the transient boiling curve. 23
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Fig. 20. Experimental heat transfer coefficients for Exp. #7 (TB – transition boiling, FB – film boiling). Fig. 18. Effect of the mass flow on the transient boiling curve.
″ ) is indicated. The maximum heat flux represents the maximum (qmax beginning of a fast cooling of the heater surface, and it occurs at approximately the same temperature where the oscillations stop, which support the assumption of a stable vapor film formation. For the bubble flow regime, therefore, the transition boiling is characterized by a constant contact of the liquid in the hot surface. Notice that Figs. 14–20 show an analysis of the last seconds of the critical heat flux experiments where the inlet mass flow, pressure and temperature are constant (as discussed in Section 3, the pressure slightly decreases after the power is reduced). The inverse heat transfer analysis provides significant insights on the critical heat flux mechanisms for different flow regimes and it can be used to better understand the post-CHF heat transfer. 6. Conclusions The flow channel and the grid spacers of the High Pressure Heat Transfer Facility were redesigned and new critical heat flux data under small modular reactor prototypical conditions were obtained. The CHF data were compared to CTF simulations and show good agreement with the CHF Look Up Table 2006 with an average error of 2% and standard deviation equal to 6%. The temperature history during the CHF experiments were used to calculate the surface temperature and heat flux using a 2D inverse heat transfer analysis approach. The results were used to analyze transient boiling curves at different flow regimes at the point of CHF and post-CHF. It is observed that after CHF the behavior of the transient boiling curve is closely related to the flow regimes and it does not follow the typical steady-state boiling curve. After CHF, for high void fraction experiments in the annular or mist flow regime, the heat flux from the wall to the fluid decreases, passes through a minimum, and starts to increases in a region where a stable film vapor is assumed to exist. For low void fraction experiments in the bubble flow regime, however, the transition region can be characterized by a constant liquid-surface contact process. The post-CHF heat transfer coefficient, in both cases, decreases after the critical heat flux and remains low and approximately constant until the power is reduced and the surface rewets.
Fig. 19. Effect of the inlet subcooling on the transient boiling curve at low local qualities.
For the conditions of Exp. #6 and #7, shown in Fig. 19, the CHF occurred at very low qualities, 0.07 and 0.06, respectively, with void fractions in the bubble (or slug) flow regime (∼0.40). It is interesting that for the low quality experiments, there is a clearly difference in the heating curve that can be divided in two regions. The first region, just after CHF, there is a transition boiling where the wall temperature increases because of the degradation of the heat transfer. In this region, however, the liquid is allowed to constantly contact the heater surface and the temperature oscillations are observed. In a second region, for temperatures higher than ∼50 °C of the saturation temperature, a stable vapor film is formed and the oscillations stop while the wall temperature keep increasing. It is important the highlight here, that the first thermocouple that indicated CHF in these experiments were at different axial locations, TC#5 for Exp. #6 and TC#7 for Exp. #7. However, for both experiments, both thermocouples #5 and #7 indicated a temperature rise higher than 30 °C, which in fact, means that the critical heat flux ocurred between these two thermocouples and difference between the local heat fluxes in these two experiments is also related to the uncertainty of the CHF location. The heat transfer coefficient for Exp. #7 is shown in Fig. 20. Because that the minimum heat flux does not clearly exists in Fig. 19, only the
Acknowledgment This work is supported by CAPES, Coordination for the Improvement of Higher Education Personnel– Brazil, Science without Borders Program, Process N. 013366/2013, and the University of Wisconsin-Madison. 24
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Appendix A Table A.1 shows the inlet conditions of the critical heat flux experiments, the average critical heat flux is the total power divided by the total heat transfer area, the local quality is the equilibrium quality and the void fraction was computed by CTF at the position of the first thermocouple that detected CHF. Both quality and void fraction are the bundle average values. Table A.2 shows the sources of the experimental error measurements.
Table A.1 Critical heat flux data. Exp. #
Mass flux kg/m2.s
hin,sub kJ/kg
Pressure MPa
CHFavg kW/m2
xlocal –
α –
TC #
3 28 15 35 2 13 14 42 43 11 9 10 16 39 23 41 4 37 33 12 40 22 36 26 27 31 32 29 30 34 1 24 25 8 17 18 19 20 5 6 21 38 7
563 746 781 764 709 784 791 770 749 778 773 776 791 768 751 767 753 751 779 784 774 773 775 1005 973 984 971 1075 1073 1504 1521 1567 1565 1348 1494 1497 1499 1504 1514 1514 1526 1505 1506
355 162 198 193 191 207 208 237 191 346 339 346 345 349 348 269 339 337 434 431 420 421 423 198 200 424 440 437 432 212 209 198 199 330 341 340 338 344 344 343 387 425 416
16.4 13.6 7.6 8.1 9.6 9.0 9.0 13.1 12.7 8.1 9.0 9.1 9.1 12.1 14.2 14.2 16.2 16.1 8.3 9.0 12.0 14.1 16.1 12.1 12.2 8.3 8.5 9.4 9.4 8.2 9.1 12.1 12.1 9.1 12.1 12.1 12.1 14.1 16.1 16.1 13.4 14.2 16.0
711 737 1107 1089 938 1056 1056 872 838 1250 1191 1207 1207 1047 997 872 838 855 1408 1325 1124 1106 972 989 972 1662 1661 1661 1662 1595 1476 1291 1291 1645 1561 1560 1560 1434 1300 1300 1577 1579 1442
0.42 0.38 0.32 0.34 0.32 0.31 0.31 0.37 0.37 0.29 0.28 0.28 0.28 0.37 0.27 0.37 0.33 0.22 0.30 0.27 0.35 0.24 0.18 0.31 0.32 0.26 0.29 0.31 0.31 0.22 0.20 0.16 0.16 0.18 0.13 0.15 0.15 0.12 0.09 0.07 0.09 0.09 0.06
0.77 0.80 0.86 0.86 0.83 0.83 0.83 0.81 0.81 0.83 0.81 0.81 0.81 0.82 0.71 0.79 0.72 0.63 0.83 0.80 0.81 0.69 0.59 0.79 0.79 0.82 0.83 0.83 0.83 0.79 0.75 0.64 0.64 0.73 0.60 0.63 0.63 0.55 0.45 0.42 0.52 0.50 0.41
10 10 5 5 5 5 5 10 9 5 5 5 5 10 6 10 10 5 5 5 10 6 5 10 10 6 7 9 9 7 7 6 6 5 6 7 7 7 7 5 5 7 7
Table A.2 Main source of uncertainties. Measurement
Source
Uncertainty
Reference documentation
Inlet Temperature
Calibration
Surface temperatures System pressure Inlet mass flux Total power
Correction factors Calibration Error propagation Error propagation in the heat loss estimation Rod geometry
1.1 °C or 0.4%, whichever is greater 5 °C 1% ∼2% ∼2%
Omega – Type K (Special limits) Duarte (2017) Greenwood (2015) Greenwood (2015) Duarte (2017)
5%
Stern Labs (2012) Duarte (2017)
Local power
25
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References
Thessaloniki 24–28 September, 2001. Kitto, J.B, 1980. Critical heat flux and the limiting quality phenomenon. In: AIChE Symposium Series – Heat Transfer, Orlando, pp. 57–78. Moon, S., Chun, S., Cho, S., Baek, W., 2005. An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions. Nucl. Eng. Des. 235, 2295–2309. NuScale Power, 2016. NuScale Standard Plant Design Certification Application. Chapter Four: Reactor, Part 2 – Tier 2, Revision 0. Available on: https://www.nrc.gov/docs/ ML1701/ML17013A274.pdf. Ozisik, M.N., Orlande, H.R.B., 2000. Inverse Heat Transfer: Fundamentals and Applications. Talyor & Francis, New York. Stern Labs, 2012. Technical Specification for 9.5 mm OD Fuel Simulators with a Cosine Axial Power Profile for the University of Wisconsin, SLTS-76, Revision 0. Salko, R.K., Avramova, M.N., 2015. COBRA-TF Subchannel Thermal-Hydraulics Code (CTF) Theory Manual – Revision 0. CASK-U-2015-0054-000. The Pennsylvania State University, U.S. Stosic, Z.V., 2005. On the frontier of boiling curve and beyond design of its origin. In: International Conference – Nuclear Energy for New Europe, Bled, Slovenia, September 5–8. Thom, J.R.S., Walker, W.M., Fallon, T.A., Reising, G.G., 1965. Boiling in sub-cooled water during flow up heated tubes for annuli. In: Symposium on Boiling Heat Transfer in Steam Generating Units and Heat Exchangers, Manchester, London. Tong, L.S., Tang, Y.S., 1997. Boiling Heat Transfer and Two-phase Flow, Second ed. Taylor & Francis, Washington, D.C. TRUCOMP, 2003. INTEMP – Inverse Heat Transfer Analysis – User’s MANUAL. USNRC, 2013. TRACE V5.840 Theory Manual, Field Equations, Solution Methods and Physical MODELS. Washington, DC, U.S. Xiong, J., Cheng, X., Yang, Y., 2015. Numerical analysis on supercritical water heat transfer in a 2 × 2 rod bundle. Ann. Nucl. Energy 80, 123–134.
Beus, S.G., 1969. A Two-Phase Turbulent Flow and Heat Transfer in Rod Bundles. American Society of Mechanical Engineering, New York, pp. 56–62. Carey, V.P., 2008. Liquid-Vapor Phase0Change Phenomena, second ed. Taylor & Francis Groups, LLC, New York, U.S. Cheng, W., Fang, X., 2014. A note on the Chen correlation of saturated flow boiling heat transfer. Int. J. Refrig. 48, 100–104. Duarte, J.P., Jo, H., Corradini, M.L., 2017. Pre- and post-CHF study at the high pressure heat transfer facility. In: ANS Winter Meeting 2017, Washington D.C. Duarte, J.P., 2017. Understanding the Minimum Film Boiling Temperature in Two-Phase Flow (Ph.D. Preliminary Report). Nuclear Engineering and Engineering Physics, University of Wisconsin-Madison. Fighetti, C.F., Reddy, D.G., 1982. Parametric Study of CHF Data. Volume 1: Compilation of Rod Bundle CHF Data Available at the Columbia University Heat Transfer Research Facility. NP-2609, Volume 1. Research Project 813. Final Report, September, 1982. Greenwood, M.S., 2015. The Critical Heat Flux at High Pressure and Low Mass Flux Prototypic of Proposed Light Water Small Modular Reactors (Ph.D. Dissertation). Nuclear Engineering and Engineering Physics Department, University of Wisconsin – Madison. Greenwood, M.S., Duarte, J.P., Corradini, M.L., 2017. Presentation and comparison of experimental critical heat flux data at conditions prototypical of light water small modular reactors. Nucl. Eng. Des. 317, 220–231. Groeneveld, D.C., Shan, J.Q., Vasic, A.Z., Leung, L.K.H., Durmayaz, A., Yang, J., Cheng, S.C., Tanase, A., 2007. The 2006 CHF look-up table. Nucl. Eng. Des. 237, 1909–1922. Igushi, T., Stovic, Z.V., Iwaki, C., 2001. Experimental investigation of boiling curve in vicinity of CHF and rewetting conditions Part 2: reflood test results and comparison to post-CHF test results. In: Proceeding of the Fifth World Conference on Experimental Heat Transfer, Fluid Mechanics, and Thermodynamics. Gree,
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Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Critical heat flux experiments and a post-CHF heat transfer analysis using 2D inverse heat transfer☆
T
⁎
Juliana P. Duartea, , Dawei Zhaob, Hangjin Joa, Michael L. Corradinia a b
Engineering Physics Department, University of Wisconsin, 1500 Engineering Drive, Madison, WI 53703, United States CCNC Key Laboratory on Nuclear Reactor Thermal Hydraulics Technology, Nuclear Power Institute of China, Chengdu 610213, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Critical heat flux (CHF) Departure from nucleate boiling (DNB) Dryout Small modular reactor Inverse heat transfer
The critical heat flux (CHF) is one of the main thermal-hydraulics safety limits in water-cooled reactors. At CHF, a film of vapor is formed on the heated wall and the wall temperature can sharply increase in a short period of time, which may lead to damage of the heater surface. In spite of many studies, the CHF mechanisms are still not well understood due to the complexity of this two-phase phenomenon and its dependence on local thermalhydraulic conditions. Two-phase boiling experiments have been conducted to observe CHF and post-CHF behavior in prototypical conditions for small modular reactors (mass flux: 560–1570 kg/m2.s, pressure: 7.6–16.4 MPa, inlet subcooling: 160–440 kJ/kg) in a 2 × 2 square rod bundle geometry with a chopped-cosine power profile at the University of Wisconsin-Madison. The fuel rods temperature history during and following CHF were used in the solution of the two-dimension inverse heat transfer problem to estimate the wall temperatures and wall heat fluxes. This analysis showed different transient boiling curves for different flow regimes that differ qualitatively and quantitatively from the typical boiling curve considered in steady-state two-phase heat transfer analysis. The experiments suggest that the inverse heat transfer analysis approach can be used to estimate the post-CHF heat transfer and to better understand the CHF mechanisms at high pressure typical of water-cooled reactors.
1. Introduction The ability to transfer heat with a minimal temperature difference is a limiting factor in heat transport systems that operate at high heat fluxes. In many industrial applications, such as power plant technologies, the heat transport systems operate with two-phase vapor-liquid flows to optimize heat transfer and minimize temperature differences. The knowledge of the heat transfer mechanisms in different two-phase flow regimes is important to define safety margins during normal and abnormal operational conditions. In these two-phase heat transport systems, such as exist in the reactor core of light water reactors (LWR), the maximum operating power is restricted to a maximum heat flux between the liquid and the heated surface. This limiting condition is known as the critical heat flux (CHF) phenomenon. At CHF, a film of vapor is formed on the heated wall and the wall temperature can sharply increase in a short period of time, which may lead to damage of the nuclear fuel rods. This phenomenon is also characterized by more mechanistic terminology known as film dryout or departure from nucleate boiling (DNB). The former term refers mostly to conditions found in boiling water reactors (BWR), where the ☆ ⁎
fuel rod surface is completed dried out downstream of the CHF point without an annular liquid film present. The latter term refers to conditions found in pressurized water reactors (PWR), where vapor bubbles accumulate near the heated wall and coalesce into a film of vapor, thereby leading to a localized increase in the heater wall temperature. The difference between the DNB and dryout is discussed by Kitto (1980) as a limiting quality phenomenon. The DNB occurs at lower quality levels while dryout occurs at higher qualities. Kitto (1980) defines a limiting quality region in which there is a considerable change in the critical heat flux for a small change in quality. The critical heat flux is predicted in thermal-hydraulic computational codes, such as TRACE (USNRC, 2013), and CTF (Salko and Avramova, 2015), by correlations from data gathered in either BWR or PWR conditions. One exception is the look up table 2006 (Groeneveld et al., 2007) that covers critical heat flux data in a large range and presents a limiting quality region. However, the thermal-hydraulic codes fail to relate the flow regime to the critical heat flux mechanisms. As shown in this paper and stated in Groeneveld et al. (2007), void fractions in the annular flow regime exist below the limiting quality. In fact, the annular flow above the limiting quality is defined by a very thin liquid film (Groeneveld et al., 2007)
A brief version of this paper was published in ANS winter meeting 2017 (Duarte et al., 2017). Corresponding author. E-mail addresses: [email protected] (J.P. Duarte), [email protected] (D. Zhao), [email protected] (H. Jo), [email protected] (M.L. Corradini).
https://doi.org/10.1016/j.nucengdes.2018.06.011 Received 15 January 2018; Received in revised form 6 June 2018; Accepted 7 June 2018 0029-5493/ © 2018 Elsevier B.V. All rights reserved.
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design is not typical of nuclear reactors but similar grid spacer designs have been used in related experimental studies (Xiong et al., 2015; Moon et al., 2005). The lateral walls are part of the flow channel and the inner walls are 0.79 mm thick. There are four grid spacers in the heated length with 12.70 mm height and two grids outside the heated length with 6.35 mm height. The power is shaped by a helical resistance filament made from Inconel 718 with a varying pitch to be close conformance with the axial profile (Eq. (1)). The filament is filled with BN which is also used as insulating sleeves between the filament and the sheath.
and the CHF mechanisms are not well understood despite of the many studies of critical heat flux (Carey, 2008). To understand the different mechanisms of vapor formation at different local qualities, new critical heat flux data were analyzed using two-dimensional inverse heat transfer. The CHF experiments were performed at the high pressure heat transfer facility built to study the heat transfer at light water small modular reactor conditions, i.e., low mass fluxes and moderate to high pressures (Greenwood et al., 2017). The flow channel was modified and new grid spacers were designed for the current work. A set of pre-CHF experiments in single-phase and two-phase flow were performed and compared to the subchannel code CTF in order to estimate the heat losses of the test section and the contact resistance of the thermocouples embed into the heater’s walls. A new set of CHF experiments are presented in this paper. The modifications have shown an improvement of the CHF prediction when compared to the look up table 2006 (Groeneveld et al., 2007).
x 1 ⎞ q (x ) = θ0 + θ1cos ⎛2·θ2 ⎛ − ⎞ ⎝ HL 2 ⎠ ⎠ ⎝
(1)
where
θ0 = 0.82, θ1 = 0.68, θ2 = 2.44
3. Pre-CHF heat transfer analysis 2. Experimental facility Steady-state experiments at different mass fluxes, pressures, inlet temperatures, and powers were performed in order to characterize the facility. The experiments were simulated using CTF (Salko and Avramova, 2015). CTF is a two-fluid computational code with three fluids fields equations (liquid, vapor, and liquid drops). It solves the energy, mass, and transversal and axial momentum equations in 1D (with capability to develop 2D and 3D models). It simulates each subchannel and each rod separately, as shown in Fig. 4, and connects each subchannel using crossflow correlations for turbulent flow. A total of seventy-eight axial nodes were used for the CTF channel. Table 2 summarizes the main model choices used in CTF simulations. The experimental range covers single-phase and two-phase flows under subcooled and saturation boiling regimes:
The High Pressure Heat Transfer Facility (HPHTF) was designed to study heat transfer under a variety of pressures in single-phase, twophase, and supercritical fluid flows (Greenwood et al., 2017). In this work, the facility was configured to examine two-phase flow conditions and critical heat flux under small modular reactor conditions. The facility (Fig. 1) consists in a test section (4) with a 2 × 2 rod bundle electrically heated and with a heated length of 2 m, a high pressure pump (1), a heat exchanger (5), an accumulator used to pressurize the system with argon gas (7), and two bypass valves (3, 6). The orifice flow meter (2) was calibrated to measure the inlet mass flow rate. Details of the loop can be found in Greenwood (2015) and Greenwood et al. (2017). The new test section flow channel and the spacer grids, which were modified for these experiments, are described in this section. The rod diameter, pitch, and power shape are comparable to typical small modular reactor designs, such as NuScale Power (2016). Each rod has ten thermocouples (TC) located in different angular and axial positions, and a cosine axial power profile. The thermocouples are located between a clad and a sheath, both made from Monel K500. The clad and sheath thickness are 0.38 mm and 0.89 mm, respectively, and the rod diameter is 9.5 mm. The inlet and outlet temperatures are measured with thermocouples Type K with 1/8 in OD located between rods #1 and #4, and the bulk temperatures are measured at six axial positions with nine Type K TC 1/16 in OD. Fig. 2 shows the TC locations with respect to the power shape and spacer grids locations, and Table 1 shows the rod and square flow channel dimensions. The new grid spacers (Fig. 3) were designed to provide support to the rods and minimally affect the flow, with no mixing vanes. This
Pressure: 7.8–16.0 MPa Mass flow: 520–2200 kg/m2.s Inlet temperature: 63–309 °C Power per rod: 1–91 kW. The calibration of the thermocouples was verified at zero power and high mass flux. At these conditions, it is expected that all thermocouples would indicate the same temperature. The thermocouples are ungrounded Type K (Ni-Cr, Ni-Al) and were purchased in different batches (inlet, outlet, bulk, and wall thermocouples). The manufacture temperature range of Type K TC is from 0 to 1250 °C with a tolerance of 1.1 °C or 0.4%, whichever is greater. The maximum deviation found was 0.9 °C for the temperature range 18–105 °C, which is within the tolerance limit. The maximum temperature of these experiments was
Fig. 1. Basic process flow diagram of the high pressure heat transfer facility (HPHTF) (Greenwood et al., 2017). 18
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Fig. 2. Chopped cosine profile, thermocouple, and spacer grid positions (right). Circumferential thermocouple locations (left). Table 1 Bundle geometry.
Table 2 CTF main model choices.
Parameter
Dimension (mm)
Parameter
Dimension (mm)
Square channel Material Thickness Width Total length Corner radius
SS316 1.98 29.92 2161.5 2.29
Rod Outer diameter Clad thickness Sheath thickness Pitch Rod-to-wall Heated length (HL)*
9.5 0.38 0.89 12.6 1.93 2000
Parameter
Model chosen
Rod friction Entrainment and deposition Mixing and void drift
λ = 0.204 Re−02 Original model Single-phase coefficients: Km = 1.4* (equilibrium distribution weighting factor in void drift model) β = 0.005 (constant turbulent mixing coefficient) Two-phase model: Beus (1969) θ = 5* (ratio between the maximum twophase turbulent mixing coefficient and the single-phase coefficient) IAPWS IF97 Radial, axial and azimuthal conduction No radiation is modeled (NRAD = 0) Off
* The heated length started 97 mm after the beginning of the square channel.
Fluid property tables Conduction model flag Number of radiation channels Flag for the Yamanouchi canister quench model (spray cooling after LOCA) Flag for the radiation heat transfer calculation Critical heat flux (CHF) Choice for nucleate boiling model DNB check option
Fig. 3. Grid spacer geometry (Duarte et al., 2017).
Off No correlation for steady state simulations Thom’s correlation Groeneveld look-up tables for steady state simulations
* Suggested values from CTF manual Revision 0 (Salko and Avramova, 2015).
̇ = Q− ̇ ṁ ·cp·(Tout−Tin) Qloss
(2)
where
Q̇ is the electrical power (kW) ṁ is the inlet mass flow (kg/s) cp is average specific heat (kJ/kg) Tout , Tin are the measured outlet and inlet temperatures (°C). The heat loss was estimated to be equal to 6% of the total power. The maximum source of uncertainties are the thermocouple calibration and the inlet mass flow calibration (Greenwood, 2015), which leads to about 2% of uncertainty by error propagation in the entahlpy rise in the fluid. The heat loss was used to estimate the local fluid conditions, i.e., the local quality and void fraction. Fig. 5 shows a schematic view of the rod thermocouples embedded between 0.38 mm clad and 0.89 mm sheath both made from Monel K500. The thermocouple diameter is 0.51 mm Inconel 600 sheaths and
Fig. 4. CTF subchannels.
limited by the maximum temperature that the loop could be kept without significant heat loss in the heat exchanger for thirty seconds. Forty-five single-phase experiments were used to estimate the heated loss of the test section defined as: 19
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of forty-three experiments is shown in Appendix A. The power limit of the facility is 100 kW per rod. The complete experimental range is: Mass flux: 560–1570 kg/m2.s Pressure: 7.6–16.4 MPa Inlet subcooling: 160–440 kJ/kg. The experimental procedure follows similar steps as in Greenwood et al. (2017). However, instead of allowing the pressure to change while searching for CHF, the inlet conditions (mass flow, temperature and pressure) are kept constant by continuous adjusting them at each power step. After the inlet conditions are set as desired for a power lower than the CHF, a steady state is achieved, and the power is increased by approximately 1 kW/rod, and for each step a new steady state condition is reached until the CHF is detected. The Labview program automatically reduces the power by a small fraction (∼5%) once the maximum TC measurement reaches a specified trip setpoint. This process continues automatically until the TCs indicate complete rewetting. Fig. 8 shows the normalized key parameters during an experimental critical heat flux run. The scale does not represent actual fractions, for example, after the power is decreased, the pressure only decreases about 0.5 MPa for an experiment at 8.0 MPa. The CHF conditions were defined as the average of one second before the CHF detection (data was collected with a frequency of 10 Hz). The average CHF (total power divided by the total heat transfer area) trends with mass flux, pressure, and inlet subcooling can be seen from Figs. 9 and 10. As it is expected for the range of these experiments, the CHF increases as the mass flux and subcooling increases, and it decreases with the pressure for this pressure range. The average heat fluxes at the CHF condition were compared to the Look Up Table (LUT2006) (Groeneveld et al., 2007), Fig. 11. The operational conditions were simulated using CTF with the bundle power continuously increased by 1 kW/min and compared to the LUT2006 until the DNBR (departure from nucleate boiling ratio) in one or more of the subchannels falls below one. At this point, the average heat flux was defined as the total power divided by the total heat transfer area. This is one method to compare CHF data as discussed in Tong and Tang (1997). The error between the data and LUT2006 is a normal distribution with average equal to 2%, standard deviation equal to 6%, and the root mean square equal to 6%. No trend was observed with the mass flux, inlet subcooling, or experimental run number. The error, however, ″ > qpred ″ ) to a non-conservative moves from a conservative zone (qexp ″ < qpred ″ ) as the pressure increases, Fig. 12. It is worth prediction (qexp noting that the data were collected in a range of low mass fluxes compared to most of the critical heat flux data in a rod bundle available in the literature. Greenwood et al. (2017) compare the first CHF data from the HPHT facility with EPRI database (Fighetti and Reddy, 1982) showing the limited number of rod bundle data available at high pressure and low mass flow conditions. As also discussed in Greenwood et al. (2017), this was one of main motivation to build the HPHT facility. This trend was not clearly seen before because of the lack of control of the experimental pressure in the previous experiments. Compared to the LUT2006, part of the new data range follows in the light grey region of Groeneveld et al. (2007) table, which means that the CHF prediction was calculated based on selected methods rather than experimental data.
Fig. 5. Schematic view of the rod thermocouples (left) and the thermal resistance model (right).
ungrounded junctions. The TC have MgO insulation except at the tips which are backfilled with BN insulation. The wall temperatures measured by the thermocouples were compared to CTF results taking into account a correction due to the conduction through the clad wall for seventy-six experiments. The difference between the measured and predicted temperatures was found to be independent of Reynolds and Prandtl numbers and to consistently increase with the local power. Therefore, a correction factor was developed as a function of the power for each thermocouple in order to model any contact resistance effect produced. The total thermal resistance is a combination of the thermocouple position with respect to the heater coil, the contact resistance between the TC and the clad, and the axial conduction through the clad wall (Duarte, 2017). After applying the correction factors, the corrected wall temperature is compared to Thom’s correlation (Thom et al., 1965) with an standard deviation of ± 5 °C, Fig. 6. For the nucleate boiling regime, Cheng and Fang (2014) and Thom et al. (1965) correlations were compared and the average difference between them were 3 °C with a standard deviation of 2 °C for this set of conditions. Thom’s correlation was chosen because its faster numerical convergence. The corrected wall temperatures are used in the inverse heat transfer analysis with an uncertainty of ± 5 °C. 4. Critical heat flux experiments Critical heat flux experiments were performed under two mass fluxes (770 and 1500 kg/m2.s), five pressure (8, 9, 12, 14, and 16 MPa), and three inlet subcoolings (200, 340 and 420 kJ/kg). Fig. 7 shows how the main experimental matrix is distributed in these conditions. Few data were collected outside the main data matrix; the complete data set
5. Post-CHF heat transfer At high pressure conditions in a bundle geometry, it is difficult to obtain visual information of critical heat flux experiments because of material limitations. The understanding of the phenomena is then build from the data we can collect and the interpretation of the results. The
Fig. 6. Comparison between predicted and measured wall temperature after applying the correction factors. 20
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Fig. 7. Main experimental data matrix.
Fig. 8. Key parameters during an experimental critical heat flux run.
Fig. 10. Critical heat flux vs. pressure for high mass flow (∼1500 kg/m2.s) at different inlet subcooling.
Fig. 9. Critical heat flux vs. pressure for low mass flow (∼770 kg/m2.s) at different inlet subcooling.
Fig. 11. Critical heat flux data compared to LUT2006.
temperature of the heater rods that determines the occurrence of CHF (by a sharp increase) is usually measured inside the heater cladding. At the CHF, the rod temperature increases because of the deterioration of the heat transfer from the wall to the liquid due to the vapor formation
or liquid film dryout. To calculate the wall temperature and the actual heat flux transfer to the liquid/vapor mixture, we need to solve the inverse heat transfer problem. The temperature increases and decreases after CHF was analyzed using an inverse heat transfer (IHT) computational model, INTEMP 21
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way, the TC measurements are used to compensate for the lack of information on the unknown boundary condition and the conduction problem can be solved. The IHT problem belong to the class of Ill-posed mathematical problems, in contradiction to the Well-posed problems in which all initial and boundary conditions are known (Ozisik and Orlande, 2000). A total of fifty axial nodes of 2.2 cm each and ten radial nodes were used from 0.9 m to the top of the heated length—only the top portion of the rod was simulated because of the location of the thermocouples. Adiabatic boundary conditions were used on the top and the bottom of the rod domain. A sensitivity analysis of the boundary conditions, mesh size, and also other numerical parameters were performed and found to be insignificant compared to other uncertainty sources (Duarte, 2017)—see Table A.2. The main source of uncertainty in the surface temperature is due to the correction factors, as discussed in Section 3, and it is estimated to be ± 5 °C. The IHT analysis calculates the surface temperature based on the two-dimensional transient conduction problem. The cladding properties are included in the solution as a temperature-depended table. A limitation of the IHT analysis is that only one boundary condition can be estimated for each temperature history and therefore, the (known and unknown) heat fluxes were discretized to seven boundary conditions which correspond to the seven axial temperature measurements. This limitation is inherent to this kind of experiment due to the limited number of thermocouples that can be placed in the rod during its fabrication. The local power error is estimated to be ± 5% according to the rod manufacturer (Stern Labs, 2012). The average heat flux used in the inverse heat transfer analysis does not differ more than 7% of the estimated local heat flux that follows the cosine shape profile, for the cases presented here. On the other hand, the 2D IHT accounts for axial conduction and provides us a better understanding of the post-CHF phenomenon as discussed in this section. For each CHF test, the temperature increase and decrease, after the power reduction, were recorded as shown in Fig. 14. The input heat flux (qin) was simulated as a known boundary condition applied at the inner sheath wall (Ri = 3.48 mm). The TC temperature data were used to calculate the wall temperature and the unknown boundary condition, i.e., the wall heat flux (qout in Fig. 14) (at = 4.75 mm).
Fig. 12. Error trend with pressure of the CHF data compared to LUT2006.
(TRUCOMP, 2003). The IHT method is a common engineering analysis approach that relies on temperature and/or heat flux measurements at a particular location for the estimation of unknown quantities, such as temperature or heat flux boundary conditions (BC), initial conditions (IC), or material properties (Ozisik and Orlande, 2000). INTEMP solves the two-dimensional nonlinear inverse heat conduction problem using the Crank-Nicolson or the Fully Implicit finite element formulation (TRUCOMP, 2003). In the particular case of this research work, the inverse problem can be understood in Fig. 13. The unknown figure to be quantified is the transferred heat flux from the rod surface to the working fluid that decreases after CHF causing the heater rod clad surface temperature to increase. Fig. 13 shows the “unknown heat fluxes”, i.e., the unknown boundary conditions on the right side, at the rod surface. The “known heat fluxes” represent the rod power applied on the sheath inner surface, i.e., the power divided by the heat transfer area. The thermocouples are shown by circles with the respective node number. In this
0.89 mm (Sheath) 0.38 mm (Clad)
TC groove BN insulaƟon Heater ribbon
INTEMP boundary condiƟons
Fig. 13. INTEMP mesh and rod domain. 22
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Fig. 16. Experimental heat transfer coefficients for Exp. #1 (NB – nucleate boiling, TB – transition boiling, FB – film boiling).
Fig. 14. Inverse heat transfer analysis for CHF for Exp. #1 (1521 kg/m2.s, 9.1 MPa, 209 kJ/kg).
The Exp. #1 is a representative example of the behavior observed for the experiments at low pressure and high local qualities. Its local equilibrium quality and void fraction are 0.20 and 0.75 (calculated by CTF at the CHF location), which means that, according to CHF flow regime map, this is a churn flow. The behavior of higher local void fraction experiments in the annular/mist flow regimes (α ≥ 0.8) is, in general, similar. For example, Fig. 17 shows the behavior of Exps. #11 and #35. These experiments were chosen because they were performed at the same pressure and mass flux and the CHF occurred at the same axial position (TC #5). The local qualities and void fractions are 0.29 and 0.83 for the Exp. #11, and 0.34 and 0.86 for Exp. #35. In fact, the maximum and minimum heat fluxes occurred at virtually the same wall temperatures and the heat transfer coefficient follows the same profile as shown in Fig. 16. Fig. 18 shows the effect of the mass flux on the transient boiling curve. Exp. #8 and #16 were chosen because in both cases the CHF occurred in the same axial position (TC#5). The local qualities and void fraction are 0.18 and 0.73 for Exp. #8, and 0.31 and 0.81 for Exp. #16. Notice that the difference between Exp.# 11 and #16 is the pressure, and the difference between the Exp. #8 and #1 is the inlet subcooling condition and the local quality. It was observed that the minimum heat flux point becomes unclear as the pressure increases and the wiggles in the heating path become more frequent as the local void fraction decreases.
Fig. 15. Heat flux versus wall temperature for Exp. #1 (1521 kg/m2.s, 9.1 MPa, 209 kJ/kg).
Note that for Exp. #1, after the CHF event, the heat flux leaving the wall significantly decreases, reaches a minimum, and starts to increase again before any power change is triggered by the control system. This behavior indicates the presence of degraded post-CHF heat transfer and passage through the minimum film boiling temperature from which a stable film boiling is formed on the wall. From this minimum point, the heat flux continuously increases with the increase of the wall temperature until the power is decreased in two steps of 5% and the wall is rewetted. Fig. 15 shows the wall heat flux versus the wall superheat temperature for the same conditions of Fig. 14. The circled points indicate the power steps at 29.5 and 31.5 s. The shape of Fig. 15, with heat fluxes higher than the CHF during the cooling of the heater wall, has been discussed before by Stosic (2005) in the analyze of Igushi et al. (2001)’s experiments. The hysteresis between the heating (bottom part of the curve) and the cooling (top part of the curve) can be explaining by solving the 1D transient coupled problem with the fluid thermal-hydraulic condition and the heat conduction in the solid material. Because Fig. 15 is a transient heat flux vs. ΔTwall curve, we will call it as a transient boiling curve. The conclusion that the minimum and maximum points in Fig. 15 represents the formation and collapse of a stable film of vapor near on the wall can also be drawn from Fig. 16. Fig. 16 shows the heat transfer ″ /(Twall−Tsat ) ] for the Exp. #1. The location of coefficient [HTC = qwall the maximum and minimum heat fluxes are indicated and one can noticed a small and nearly constant HTC between these two points.
Fig. 17. Effect of the inlet subcooling on the transient boiling curve. 23
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Fig. 20. Experimental heat transfer coefficients for Exp. #7 (TB – transition boiling, FB – film boiling). Fig. 18. Effect of the mass flow on the transient boiling curve.
″ ) is indicated. The maximum heat flux represents the maximum (qmax beginning of a fast cooling of the heater surface, and it occurs at approximately the same temperature where the oscillations stop, which support the assumption of a stable vapor film formation. For the bubble flow regime, therefore, the transition boiling is characterized by a constant contact of the liquid in the hot surface. Notice that Figs. 14–20 show an analysis of the last seconds of the critical heat flux experiments where the inlet mass flow, pressure and temperature are constant (as discussed in Section 3, the pressure slightly decreases after the power is reduced). The inverse heat transfer analysis provides significant insights on the critical heat flux mechanisms for different flow regimes and it can be used to better understand the post-CHF heat transfer. 6. Conclusions The flow channel and the grid spacers of the High Pressure Heat Transfer Facility were redesigned and new critical heat flux data under small modular reactor prototypical conditions were obtained. The CHF data were compared to CTF simulations and show good agreement with the CHF Look Up Table 2006 with an average error of 2% and standard deviation equal to 6%. The temperature history during the CHF experiments were used to calculate the surface temperature and heat flux using a 2D inverse heat transfer analysis approach. The results were used to analyze transient boiling curves at different flow regimes at the point of CHF and post-CHF. It is observed that after CHF the behavior of the transient boiling curve is closely related to the flow regimes and it does not follow the typical steady-state boiling curve. After CHF, for high void fraction experiments in the annular or mist flow regime, the heat flux from the wall to the fluid decreases, passes through a minimum, and starts to increases in a region where a stable film vapor is assumed to exist. For low void fraction experiments in the bubble flow regime, however, the transition region can be characterized by a constant liquid-surface contact process. The post-CHF heat transfer coefficient, in both cases, decreases after the critical heat flux and remains low and approximately constant until the power is reduced and the surface rewets.
Fig. 19. Effect of the inlet subcooling on the transient boiling curve at low local qualities.
For the conditions of Exp. #6 and #7, shown in Fig. 19, the CHF occurred at very low qualities, 0.07 and 0.06, respectively, with void fractions in the bubble (or slug) flow regime (∼0.40). It is interesting that for the low quality experiments, there is a clearly difference in the heating curve that can be divided in two regions. The first region, just after CHF, there is a transition boiling where the wall temperature increases because of the degradation of the heat transfer. In this region, however, the liquid is allowed to constantly contact the heater surface and the temperature oscillations are observed. In a second region, for temperatures higher than ∼50 °C of the saturation temperature, a stable vapor film is formed and the oscillations stop while the wall temperature keep increasing. It is important the highlight here, that the first thermocouple that indicated CHF in these experiments were at different axial locations, TC#5 for Exp. #6 and TC#7 for Exp. #7. However, for both experiments, both thermocouples #5 and #7 indicated a temperature rise higher than 30 °C, which in fact, means that the critical heat flux ocurred between these two thermocouples and difference between the local heat fluxes in these two experiments is also related to the uncertainty of the CHF location. The heat transfer coefficient for Exp. #7 is shown in Fig. 20. Because that the minimum heat flux does not clearly exists in Fig. 19, only the
Acknowledgment This work is supported by CAPES, Coordination for the Improvement of Higher Education Personnel– Brazil, Science without Borders Program, Process N. 013366/2013, and the University of Wisconsin-Madison. 24
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Appendix A Table A.1 shows the inlet conditions of the critical heat flux experiments, the average critical heat flux is the total power divided by the total heat transfer area, the local quality is the equilibrium quality and the void fraction was computed by CTF at the position of the first thermocouple that detected CHF. Both quality and void fraction are the bundle average values. Table A.2 shows the sources of the experimental error measurements.
Table A.1 Critical heat flux data. Exp. #
Mass flux kg/m2.s
hin,sub kJ/kg
Pressure MPa
CHFavg kW/m2
xlocal –
α –
TC #
3 28 15 35 2 13 14 42 43 11 9 10 16 39 23 41 4 37 33 12 40 22 36 26 27 31 32 29 30 34 1 24 25 8 17 18 19 20 5 6 21 38 7
563 746 781 764 709 784 791 770 749 778 773 776 791 768 751 767 753 751 779 784 774 773 775 1005 973 984 971 1075 1073 1504 1521 1567 1565 1348 1494 1497 1499 1504 1514 1514 1526 1505 1506
355 162 198 193 191 207 208 237 191 346 339 346 345 349 348 269 339 337 434 431 420 421 423 198 200 424 440 437 432 212 209 198 199 330 341 340 338 344 344 343 387 425 416
16.4 13.6 7.6 8.1 9.6 9.0 9.0 13.1 12.7 8.1 9.0 9.1 9.1 12.1 14.2 14.2 16.2 16.1 8.3 9.0 12.0 14.1 16.1 12.1 12.2 8.3 8.5 9.4 9.4 8.2 9.1 12.1 12.1 9.1 12.1 12.1 12.1 14.1 16.1 16.1 13.4 14.2 16.0
711 737 1107 1089 938 1056 1056 872 838 1250 1191 1207 1207 1047 997 872 838 855 1408 1325 1124 1106 972 989 972 1662 1661 1661 1662 1595 1476 1291 1291 1645 1561 1560 1560 1434 1300 1300 1577 1579 1442
0.42 0.38 0.32 0.34 0.32 0.31 0.31 0.37 0.37 0.29 0.28 0.28 0.28 0.37 0.27 0.37 0.33 0.22 0.30 0.27 0.35 0.24 0.18 0.31 0.32 0.26 0.29 0.31 0.31 0.22 0.20 0.16 0.16 0.18 0.13 0.15 0.15 0.12 0.09 0.07 0.09 0.09 0.06
0.77 0.80 0.86 0.86 0.83 0.83 0.83 0.81 0.81 0.83 0.81 0.81 0.81 0.82 0.71 0.79 0.72 0.63 0.83 0.80 0.81 0.69 0.59 0.79 0.79 0.82 0.83 0.83 0.83 0.79 0.75 0.64 0.64 0.73 0.60 0.63 0.63 0.55 0.45 0.42 0.52 0.50 0.41
10 10 5 5 5 5 5 10 9 5 5 5 5 10 6 10 10 5 5 5 10 6 5 10 10 6 7 9 9 7 7 6 6 5 6 7 7 7 7 5 5 7 7
Table A.2 Main source of uncertainties. Measurement
Source
Uncertainty
Reference documentation
Inlet Temperature
Calibration
Surface temperatures System pressure Inlet mass flux Total power
Correction factors Calibration Error propagation Error propagation in the heat loss estimation Rod geometry
1.1 °C or 0.4%, whichever is greater 5 °C 1% ∼2% ∼2%
Omega – Type K (Special limits) Duarte (2017) Greenwood (2015) Greenwood (2015) Duarte (2017)
5%
Stern Labs (2012) Duarte (2017)
Local power
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