Analogy based modeling of natural convection

This research is an extension of previous work on the development of an integrator or resistance-capacitance circuit analogy for natural convection. As a part of a larger project to enhance transport phenomenon on a micro-scale using radiation, this work studied the phenomenon of natural convection. Using experimental techniques and numerical simulations (FLUENT code), it investigated the transient response of a natural convection system. It proposes an integrator circuit analogy for a natural convection system. Experimental investigation with three different fluids indicated that the characteristic time constant of the system is related to the Prandtl number of the fluid. The project also investigated the effect of gravity and fluid viscosity --Abstract, page iv

Experimental and computational investigation of flow of pebbles in a pebble bed nuclear reactor

The Pebble Bed Reactor (PBR) is a 4th generation nuclear reactor which is conceptually similar to moving bed reactors used in the chemical and petrochemical industries. In a PBR core, nuclear fuel in the form of pebbles moves slowly under the influence of gravity. Due to the dynamic nature of the core, a thorough understanding about slow and dense granular flow of pebbles is required from both a reactor safety and performance evaluation point of view. In this dissertation, a new integrated experimental and computational study of granular flow in a PBR has been performed. Continuous pebble re-circulation experimental set-up, mimicking flow of pebbles in a PBR, is designed and developed. Experimental investigation of the flow of pebbles in a mimicked test reactor was carried out for the first time using non-invasive radioactive particle tracking (RPT) and residence time distribution (RTD) techniques to measure the pebble trajectory, velocity, overall/zonal residence times, flow patterns etc. The tracer trajectory length and overall/zonal residence time is found to increase with change in pebble\u27s initial seeding position from the center towards the wall of the test reactor. Overall and zonal average velocities of pebbles are found to decrease from the center towards the wall. Discrete element method (DEM) based simulations of test reactor geometry were also carried out using commercial code EDEM and simulation results were validated using the obtained benchmark experimental data. In addition, EDEM based parametric sensitivity study of interaction properties was carried out which suggests that static friction characteristics play an important role from a packed/pebble beds structural characterization point of view. To make the RPT technique viable for practical applications and to enhance its accuracy, a novel and dynamic technique for RPT calibration was designed and developed. Preliminary feasibility results suggest that it can be implemented as a non-invasive and dynamic calibration methodology for RPT technique which will enable its industrial applications. --Abstract, page iii

Analogy Based Modeling for Natural Convection [abstract]

Only abstract of poster available.Track I: Power GenerationNatural convection is an important phenomenon for many engineering systems including nuclear reactors. Present day nuclear reactors rely on the phenomenon for decay heat removal. While advanced CANDU-X would incorporate natural circulation for enhanced passive heat removals system to ensure safety, while other GEN IV designs also use natural convection as their main mode of heat removal. For this reason, transient analysis of natural convection has been an area of significant interest. As a part of our larger project to enhance transport phenomenon at the micro-scale using radiation, we studied the phenomenon of natural convection. Using experimental techniques and numerical simulation (FLUENT code) transient response of a natural convection system was investigated. An Integrator Circuit analogy was proposed for natural convection system. Experimental investigation with three different fluids indicated that the characteristic time constant of the system is related to the Prandtl number of fluid. Moreover, effect of gravity and fluid viscosity were also investigated. Simulations results suggest that natural convection system acts as a “Low Pass” filter. Transmission characteristics of natural convection system were found to be a function of both fluid properties and the flow characteristics. Transmission factor was found to be a strong function of temperature oscillation frequency. Our numerical simulations also suggested that in additional to the thermal energy stored in the system, for natural convection energy is also stored in the form of kinetic energy of the fluid set in motion due to buoyancy. This energy is found to be related to system's Rayleigh number

Extension of RC Circuit Analogy for Natural Convection

Present study investigated the analogy further by redrawing the equivalent circuit as shown in the Fig.1 . The corresponding resistance is drawn as a combination of two parallel resistances. The fixed resistance (R) is due to the conduction, while the variable resistance (R,h)is due to convection and depends on state of flow. Likewise, the capacitor of the equivalent circuit is also drawn as two parallel capacitors. Cth represents the thermal capacitance of the system, constant and depends on the fluid properties only. CK E is the Kinetic Energy Capacitance of the system which for a given geometry depends on the fluid properties as well as the flow characteristics

Hybrid Dynamic Radioactive Particle Tracking (RPT) Calibration Technique for Multiphase Flow Systems

The radioactive particle tracking (RPT) technique has been utilized to measure three-dimensional hydrodynamic parameters for multiphase flow systems. An analytical solution to the inverse problem of the RPT technique, i.e. finding the instantaneous tracer positions based upon instantaneous counts received in the detectors, is not possible. Therefore, a calibration to obtain a counts-distance map is needed. There are major shortcomings in the conventional RPT calibration method due to which it has limited applicability in practical applications. In this work, the design and development of a novel dynamic RPT calibration technique are carried out to overcome the shortcomings of the conventional RPT calibration method. The dynamic RPT calibration technique has been implemented around a test reactor with 1foot in diameter and 1 foot in height using Cobalt-60 as an isotopes tracer particle. Two sets of experiments have been carried out to test the capability of novel dynamic RPT calibration. In the first set of experiments, a manual calibration apparatus has been used to hold a tracer particle at known static locations. In the second set of experiments, the tracer particle was moved vertically downwards along a straight line path in a controlled manner. The obtained reconstruction results about the tracer particle position were compared with the actual known position and the reconstruction errors were estimated. The obtained results revealed that the dynamic RPT calibration technique is capable of identifying tracer particle positions with a reconstruction error between 1 to 5.9 mm for the conditions studied which could be improved depending on various factors outlined here

Experimental Investigation of the Overall Residence Time of Pebbles in a Pebble Bed Reactor (PBR) using Radioactive Pebble

The granular flow of pebbles in a pebble bed reactor (PBR) under the influence of gravity is a dense granular flow with long-lasting frictional contacts. The basic governing physics is not fully understood and hence the dynamic core of a PBR and non-idealities associated with pebbles flow inside the reactor core are of non-trivial significance from the point of view of safety analyses, licensing, and thermal hydraulics. In the current study, overall and zonal pebbles residence time investigation is carried out by implementing noninvasive radioisotope-based flow visualization measurement techniques such as residence time distribution (RTD) and radioactive particle tracking (RPT). The characteristics of overall pebble residence time/transient number, zonal residence time, and the z-component of average zonal velocities at different initial seeding positions of a tracer particle have been summarized. It is found that the overall pebbles residence time/transient number increases (the z-component of average zonal velocities decreases) from the center towards the reactor wall. Also, pebbles\u27 zonal residence time results (the whole core is divided into three zones) which provide more insight and understanding about PBR core dynamics have been reported. The benchmark data provided could be used for assessment of commercial/in-house computational methodologies related to granular flow investigations

Assessment of Performing Experimental Investigation on a Pebble Bed Modular Reactor (PBMR) As a Static Packed Bed Approximation

Moving bed reactors have a wide range of applications in the chemical, petrochemical, and alternative energy industries in a special situation where there is a need to either continuously recirculate or replace solid particles catalysts. They are also under consideration as one of the 4th generation nuclear reactors known as pebble bed modular reactor (PBMR). In this work a continuous cold flow pebble recirculation experimental set-up, mimicking the flow of pebbles in a PBMR, is designed, developed, and tested at Missouri S&T. A unique experimental work has been performed on assessment of the possibility of using pebble bed modular reactor (PBMR) as static packed bed approximation for the needed experimental investigation. For this purpose, a radioactive particle tracking (RPT) technique is implemented around the continuous pebble recirculation experimental set-up, to compare the packing characteristics of static and moving pebble beds. The photopeak counts during RPT calibration were collected by placing radioactive particle (tracer) at different positions in the test reactor under different operating conditions of moving and static conditions. The photopeak counts between moving and static conditions show that attenuation characteristics of the medium in between tracer and detectors are not changing significantly due to movement of pebbles. This confirms that PBMR could be well approximated by static packed beds for experimental investigation which simplify the needed experimentation to advance PBMR technology and commercialization. Obtained results are serving as a unique benchmark data for an evaluation of the contact force model that used in the discrete element method (DEM) based simulations

Experimental Investigation of Pebble Flow Dynamics using Radioactive Particle Tracking Technique in a Scaled-Down Pebble Bed Modular Reactor (PBMR)

The Pebble Bed Modular Reactor (PBMR) is a type of very-high-temperature reactor (VHTR) that is conceptually very similar to moving bed reactors used in the chemical and petrochemical industries. In a PBMR core, nuclear fuel is in the form of pebbles and moves slowly under the influence of gravity. In this work, an integrated experimental and computational study of granular flow in a scaled-down cold flow PBMR was performed. A continuous pebble re-circulation experimental set-up, mimicking the flow of pebbles in a PBMR was designed and developed. An experimental investigation of pebble flow dynamics in a scaled down test reactor was carried out using a non-invasive radioactive particle tracking (RPT) technique that used a cobalt-60 based tracer to mimic pebbles in terms of shape, size and density. A cross-correlation based position reconstruction algorithm and RPT calibration data were used to obtain results about Lagrangian trajectories, the velocity field, and residence time distributions. The RPT technique results a serve as a benchmark data for assessing contact force models used in the discrete element method (DEM) simulations

Discrete Element Method-Based Investigations of Granular Flow in a Pebble Bed Reactor

In a pebble bed reactor (PBR) core, nuclear fuel in the form of pebbles moves slowly under the influence of gravity. Due to the dynamic nature of the core, a thorough understanding about slow and dense granular flow of pebbles is required from both a reactor safety point of view and a performance evaluation point of view. In the current study, validation of discrete element method (DEM)-based simulation for the pebble flow in a PBR was carried out. Validation of DEM-based simulations necessitates validation of the employed numerical method of simulating packed structure. Hence, a parametric sensitivity study of packing interaction properties was initially conducted and also validation of the numerical method simulating packed structure at first. The parametric sensitivity analysis suggests that static friction characteristics play an important role from a packed/pebble bed structural characterization point of view. In addition, the simulated packed structure approach has shown a good agreement with the available benchmark data. Afterward, the effect of two different half-cone angles of 30 deg and 60 deg on pebble flow field in a PBR was studied by EDEMTM-based simulations. Results of streamlines, velocity radial profiles, and direct observation of discharge indicated a plug-type flow in the upper cylindrical region, whereas results indicated converging-type flow near the bottom conical region. EDEMTM results of granular flow were validated against experimental benchmark data and show a fair agreement in terms of Lagrangian trajectories and velocity profile. Therefore, this validated EDEMTM-based simulation can be used to obtain reliable results of pebble dynamics in a PBR and to enhance understanding of this phenomenon in a PBR. However, additional experimental investigations are recommended to be carried out for different sizes of test reactors, different bottom cone angles, and different sizes of pebbles to further assess DEM simulation results before using them for full-scale reactor simulations