Similitude of forced convection heat transfer of Dowtherm A and of Li2BeF4 molten salt in cylindrical tubes By Dajie Sun A thesis submitted in partial satisfaction of the requirements for the degree of Master of Science in Nuclear Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Prof. Per Peterson, Chair Prof. Karl van Bibber Prof. Jasmina Vujic Summer 2017 The University of California Berkeley Department of Nuclear Engineering Content Symbols ......................................................................................................................................................................................... ii Abstract .......................................................................................................................................................................................... 1 Chapter 1 Introduction ............................................................................................................................................................. 1 Chapter 2 Description of Experiments ................................................................................................................................ 4 Chapter 3 Theoretical model for data reduction ............................................................................................................. 7 Chapter 4 Fitting Method ........................................................................................................................................................ 9 Chapter 5 Results .................................................................................................................................................................... 13 Chapter 6 Error and Uncertainty Analysis ....................................................................................................................... 17 Chapter 7 Conclusions ........................................................................................................................................................... 20 Acknowledgments ................................................................................................................................................................... 22 References ................................................................................................................................................................................. 22 Appendix .................................................................................................................................................................................... 24 Appendix A Physical properties of Dowtherm A ................................................................................................. 24 Appendix B Matlab code to calculate the Nusselt number ............................................................................. 26 Appendix C Mathematica code for Power Regression with more than 2 parameters. .......................... 34 Appendix D OriginLab procedure for power regression with less than 3 parameters. .......................... 34 i The University of California Berkeley Department of Nuclear Engineering Symbols NuD Local Nusselt number NuR Reduced Nusselt numer Pr Prandtl number Re Reynolds number x Position along the pipe L Length of the heating pipe D Inside diameter of the pipe Dynamic viscosity of the fluid w Dynamic viscosity of the fluid at the wall temperature Qm Mass flow rate Pt Total heating power of the test section Tin Flow temperature at the inlet Tout Flow temperature at the outlet c p Specific heat of the fluid i Sequence Number of each node (positon of each thermocouple) hi Local heat transfer coefficient of ith section of the pipe (between node i+1 and i) kT fi, Thermal conductivity of the fluid at the temperature of Tfi, Electrical resistance of the pipe Ti Temperature of the thermocouple at ith node Tfi, Flow temperature at the position of ith node st li Distance between the 1 node and the ith node. li Distance between the ith node and the (i+1)th node Uncertainty Gz The Graetz number ii The University of California Berkeley Department of Nuclear Engineering Abstract Similitude of forced convection heat transfer of Dowtherm A and of Li2BeF4 molten salt in cylindrical tubes by Dajie Sun Master of Science University of California, Berkeley Professor Per Peterson, Chair Dowtherm A, a heat transfer oil used extensively in industry, has been found to be an attractive simulant fluid to study convective heat transfer phenomena for the high temperature molten salt flibe (Li2BeF4). This thesis analyzes extensive data for forced convection heat transfer in cylindrical channels using the heat transfer oil Dowtherm A oil, comparing this to data collected for flibe at Oak Ridge National Laboratory in the 1970’s. The use of Dowtherm enables reduced temperature, reduced scale experiments, which greatly reduces experimental costs compared to working with actual salts. Forced convection heat transfer data for flibe collected at ORNL is limited to experiments performed above 680°C, with a maximum Prandtl number of 14. Since molten salt reactors can commonly operate at lower temperatures, one is interested in also predicting convective heat transfer at Prandtl number up to 20 and above. This paper presents recent progress in the measurement and correlation of forced heat transfer coefficients of Dowtherm A with Prandtl number up to 53, including correlations for laminar, transition and turbulent flow regimes and for entrance regions. Data was collected with Dowtherm in a 0.00546 m vertical circular tube for the following range of variables: Reynolds number 280-200,000 Prandtl number 8.5-53 Flow temperature (°C) 30-170 Within these ranges, the Nusselt number was calculated based upon the experimental data. Correlations of the experimental data resulted in these equations: 0.0816 0.14 1.098 0.33 x x NuD 0.00250 Re Pr , 19 214 D w D with an average absolute deviation of 12.7% for 280<Re < 3,800; 0.14 0.82341 1/3 Nu 0.0184 Re Pr w with an average absolute deviation of 4.3% for 3,400<Re < 50,000; 1 The University of California Berkeley Department of Nuclear Engineering 0.14 1.02712 1/3 Nu 0.00195Re Pr w with an average absolute deviation of 5.2% for 50,000<Re < 200,000. Keywords: Heat transfer, Dowtherm A, forced convection, similitude 2 The University of California Berkeley Department of Nuclear Engineering Chapter 1 Introduction Because molten salts can transfer heat at low pressure and high temperature, and are chemically stable, molten salts are attractive heat transfer fluids. The molten salt flibe (Li2BeF4) has particularly attractive properties and has been studied extensively for use in molten salt cooled and fueled reactors [1][2]. A key problem for design and licensing is predicting convective heat transfer under natural circulation and forced convection conditions. Bardet and Peterson found that heat transfer oils such as Dowtherm A can serve as effective simulant fluids for the molten salt flibe and other fluoride salts [4]. By selecting appropriate length, velocity, and temperature scaling values it is possible to match the Prandtl (Pr), Froude number (Fr), Reynolds (Re) and Grashof (Gr) numbers of Flibe simultaneously in geometrically scaled experiments operating at low-temperature. This scaling also reduces length and velocity scales of the reactor flow, and thus can be applied to integral effects testing as well as separate effects testing [3]. Rohit Upadhya and Shannon Bragg-Sitton [6] provide a preliminary scaling analysis of a 300MWth FHR-HTSE’s primary loop, conducted an analysis to see whether Dowtherm A would match the Prandtl with a core temperature range of 800℃-850℃. Because results are expected to be used in reactor safety licensing analysis, it is important confirm the similitude between convective heat transport phenomena with flibe, and the simulant Dowtherm A. This masters thesis presents data analysis to compare forced convection heat transfer in cylindrical tubes, comparing data collected from recent experiments performed using Dowtherm A to earlier experiments performed at Oak Ridge National Laboratory with flibe [13]. The Dittus–Boelter (D-B) equation [10] is a popular and preferred version to calculate the heat transfer coefficient: 0.8 n NuD 0.023Re Pr (1) where NuD is the Nusselt number, Re the Reynolds number, and Pr the Prandtl number, and the exponent n takes the value 0.4 for heating (Tw> Tf) and 0.3 for cooling (Tw< Tf). The D-B equation is valid for the range of conditions 0.7 Pr 160 Re 10000 L 10 D Considering the effect of the temperature difference between the pipe wall and the flow, which changes the viscosity, Sieder and Tate[11] recommended: 1 The University of California Berkeley Department of Nuclear Engineering 0.14 0.8 1/3 NuD 0.027 Re Pr (2) w 0.7 Pr 160700 Re 10000 L 10 D The Dow Chemical company recommends that the Sieder and Tate equation be used for Dowtherm A [12]. In the 1970s, heat transfer was measured experimentally at Oak Ridge National Laboratory (ORNL) [13] for proposed molten salt reactors. The physical properties of molten salt fuel and Flibe are listed in Table 1 [5]: Table 1 Physical Property of Flibe and Molten Salt for Reactor Fuel Molten salt reactor fuel Flibe Density(g/cm3) 3.3754 2.012 Heat Capacity, Cp (J/(kg·K)) 1360 2386 Thermal Conductivity (W/(m℃)) 0.8 1.0 Dynamical Viscosity,μ(10-3kg/(m·s)) 27.72 17.0 Melt Point(℃) 479 459