Gravity stratified mixed convection in liquid metal pools: implications and experimental interpretation for LMFRs - Ward, Brendan C. (Kansas State University, 2020)
Understanding stratification and mixing in large enclosures, how buoyancy effects the dispersion of concentration or temperature, plays an important role in safety analyses for the gamut of nuclear reactor types. In the upper plena of pool-type liquid metal cooled fast reactors (LMFRs) this phenomenon becomes more complex due to the extremely strong thermal diffusion (Prandtl number, Pr « 1) of the liquid metal coolant, making safety envelope predictions difficult. High fidelity experimental data on thermal stratification is needed to validate and improve safety analysis codes for LMFRs. Design of an experimental facility and instrumentation becomes complicated with liquid sodium, the preferred coolant for U.S. based LMFR designs. A surrogate fluid simplifies the design and operation considerably, providing the flexibility to obtain high quality measurements. The scaled experimental facility, the Gallium Thermal-hydraulic Experiment (GaTE), is designed using verified models based upon similarity analysis and physical constraints of the advanced sensors. Liquid gallium (Pr≈0.025) is chosen as a surrogate for liquid sodium (Pr≈0.005) considering scaling factors, material handling constraints, and the capabilities of the sensors. The advanced sensors are key to understanding stratification in the plenum. Distributed temperature is captured using fiber-optic interferometry based on the principles of Rayleigh backscattering. This technique allows for higher temporal resolution (22 Hz) and finer spatial pitch (2.6 mm throughout) than those employed by previous research. Distributed velocity is measured using ultrasonic Doppler velocimetry (UDV) since optical techniques are not possible with the opaque liquid metal. The pulsed UDV technique, capturing information at 19 Hz and 1 mm pitch, also provides the necessary high resolution, distributed information. These higher resolutions and distributed sensing allow investigation of key transient information. The higher temporal resolution allows the fluctuating component of temperature, T’, and velocity, w’, to be captured to relevant scales; the spatial resolution allows for accurate representation of their respective gradients. A variety of tests are needed to measure these parameters. Forced-circulation isothermal tests benchmark the velocity behavior without buoyant influences. Conversely, natural-circulation driven flows provide affirmation of loop dynamics under various ‘core’ conditions. Cold step-transients, with injection of colder fluid at the bottom of the plenum, investigate the transition where flow fluctuations can overcome the restorative buoyant forces. The output of these tests, simulated or experimental, provide the framework for the scaling analysis, model development, and model validation. The scaling analysis investigated the effects of differences in Pr, average temperatures, size, and shape of the upper plenum on scaling distortions. These are computed with the help of model calculations and output parameters such as eddy thermal diffusivity (κτ =(w'T') ̅/∂T/∂z), quantifying the effect on the temporal temperature evolution during model transients. This parameter is empirically modeled as a function of geometry, material properties, flow, and temperature conditions of the jet entering the plenum. The capabilities of the GaTE allow maneuvering and monitoring of the flux Richardson number (Rif = (gβ(w^' T^' ) ̅)/((u'w') ̅ ∂w/∂z)) which signifies the transition from planar to fluctuating thermally stratified front. With the background for the unique spectral behavior in liquid metal outlined and verified, the framework for explaining the fluctuations on the thermal front is established. Using the spectral turbulence data, a map of __ is constructed and compares well with the scaling analysis empirical model and the molecular diffusivity. Experimental data match global expectations of the empirically modeled and measured turbulent Prandtl number (Prτ = ((u'w') ̅/∂w/∂z)/( (w'T') ̅/∂T/∂z)). The behavior unique to liquid metal thermal stratification is explained: the relatively weak influence of buoyancy due to the strong horizontal diffusion of temperature; and the sustained turbulent action of the momentum in the inertial-diffusive governed flows increases the κτ despite relatively calm thermal behavior. Throughout this dissertation, the understanding of κτ and Prτ have been used, interpreted, and expanded upon. Liquid metal’s uniquely low Pr in stably stratified turbulence was explored and understood through specialized advanced sensors, allowing a deeper fundamental understanding for higher accuracy in system level safety analysis codes for LMFRs.
Keywords: Liquid metal; Thermal stratification; Mixed convection