Transactions of the American Nuclear Society, 1986
Current efforts are under way to develop and evaluate numerical algorithms for the parallel solut... more Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required.
Numerical solutions involving finite difference representations of the equations governing fluid ... more Numerical solutions involving finite difference representations of the equations governing fluid flow, heat conduction, and diffusion processes (including neutron diffusion) usually consist of solving large sparse matrix equations. These matrix equations can be recast into M smaller coupled matrix equations amenable to solution by using M multiple computer processors operating in parallel. A special form of the fluids equations commonly used in nuclear reactor thermal-hydraulic analysis, i.e., one-dimensional flow in closed loop geometry is emphasized. Parallel algorithms for solving these equations are developed and evaluated in terms of computational speed against conventional solutions on a serial machine. Timing studies are performed to assess the efficiency of these methods and to determine the optimum number of parallel processors for these applications. Algorithmes de traitement en parallele pour resoudre les equations de Navier-Stokes d'apres la methode des differences finies
Drift-flux models can be used to describe two-phase-flow systems when explicit representation of ... more Drift-flux models can be used to describe two-phase-flow systems when explicit representation of the relative phase motion is not required. In these models, relative phase velocity is described by flowregime-dependent, semiempirical models. Numerical stability of the mixture drift-flux equations is examined for different semi-implicit time discretization schemes. Representative flow-regime-dependent drift-flux correlations are considered, and analytic stability limits are derived based on these correlations. The analytic stability limits are verified by numerical experiments run in the vicinity of the predicted stable boundaries. It is shown that the stability limits are strong functions of the time-level specification and functional form chosen for the relative phase velocity. It is also shown that the mixture Courant limit normally associated with these methods is insufficient for ensuring a stable numerical scheme.
Mixture models are commonly used in the simulation of transient two-phase flows as simplification... more Mixture models are commonly used in the simulation of transient two-phase flows as simplifications of six-equation models, with the drift-flux models as a common way to describe relative phase motion. This is particularly true in simulator and control system modeling where solutions that are faster than real time are necessary, and as a means for incorporating thermal-hydraulic feedback into steady-state and transient neutronics calculations. Variations on semi-implicit finite difference schemes are some of the more commonly used temporal discretization schemes. The maximum timestep size associated with these schemes is normally assumed to be limited by stability considerations to the material transport time across any computational cell (Courant limit). In applications requiring solutions that are faster than real time or the calculation of thermal-hydraulic feedback in reactor kinetics codes, time-step sizes that are restricted by the material Courant limit may result in prohibitive run times. A Courant violating scheme is examined for the mixture drift-flux equations, which for rapid transients is at least as fast as classic semi-implicit methods and for slow transients allows timestep sizes many times greater than the material Courant limit.
Computer models w i l l be used t o s imulate the performance o f a number o f TES/heat pump conf... more Computer models w i l l be used t o s imulate the performance o f a number o f TES/heat pump conf igura t ions . Models w i l l be based on e x i s t i n g performance data o f heat pump components, a v a i l ab le b u i l d i n g thermal 1 oad computational procedures, and general ized TES subsystem design. D i f f e r e n t e l e c t r i c i t y r a t e s t ruc tures w i l l be assumed f o r each s i t e . L i f e c y c l e costs f o r each s i t e , con f i gu ra t i on and r a t e s t r u c t u r e w i l l then be computed.
Interest is in developing neutronic and thermal-hydraulic computer programs that execute efficien... more Interest is in developing neutronic and thermal-hydraulic computer programs that execute efficiently on advanced engineering work stations. Engineering work stations are characterized by a 32-bit arithmetic processor, graphics capabilities, and networking capabilities. These attributes allow an engineer to solve substantive problems in a graphical interactive environment with shared resources available via networking. An advanced engineering work station is further characterized
The thermal-hydraulic code FLOC has been developed to investigate the vector and multi-CPU perfor... more The thermal-hydraulic code FLOC has been developed to investigate the vector and multi-CPU performance of advanced computer systems. The FLOC code solves the area-averaged Navier-Stokes equations using a semi-implicit formulation that produces a linear system in terms of the spatial pressure distribution. This code was written on a VAX and transported to a CRAY X-MP, where it was optimized for
A thermal-hydraulics code named FLOC, developed specifically to investigate parallel numerical al... more A thermal-hydraulics code named FLOC, developed specifically to investigate parallel numerical algorithms for solution of the area-averaged Navier-Stokes equations, was originally written to run on a VAX minicomputer and later implemented on a CRAY X-MP. The FLOC code utilizes a semiimplicit formulation to produce a linear system in the spatial pressure distribution at each time step. As transported, the code ran at just over 4 MFLOPs and required 25 CPUs to complete a 10-s pump startup transient for a 72-volume/84-junction two-loop representation of a pressurized water reactor. After restructuring to enhance vectorization by the CRAY vectorizing compiler (version 1.15), the same transient ran at > 23 MFLOPs in < 4 CPUs using fixed time steps. The same simulation allowing variable time steps ran in 0.7 s, more than 10 times faster than real time. The FLOC code consists of eight subroutines, which are called at each time step, and several additional subroutines, which perform i...
For the past several years, a full plant engineering simulation code has been under development i... more For the past several years, a full plant engineering simulation code has been under development in the Nuclear Engineering Department at North Carolina State University to simulate the dynamic response of Pressurized Water Reactor Systems. The software is used in the Department's Reactor Systems course, as well as a number of other undergraduate courses to demonstrate the effectiveness of the plants control and protection systems and illustrate transient systems behavior during normal and off-normal operating conditions. The software has served as the basis of a Simulation Laboratory within the Department with the goal of providing a convenient, interactive platform for the design and analysis of reactor systems.
Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotr... more Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotron water targets. Previous heat transfer models assumed either a distribution of void under saturation conditions [1] or a static volumetric heat distribution [2]. This work explores the coupling of Monte Carlo radiation transport and Computation Fluid Dynamics (CFD) software in a computational model of the BTI Targetry visualization target [3]. In a batch water target, as the target medium is heated by energy deposition from the proton beam, a non-uniform density distribution develops. Production target operation is ultimately limited by the range thickness of the target under conditions of reduced water density. Since proton range is a function of target density, the system model must include the corresponding change in the volumetric heat distribution. As an initial attempt to couple the radiation transport and fluid dynamics calculations, the scope of this work was limited to subcool...
Approximately 19% of the electricity produced in the United States comes from nuclear power plant... more Approximately 19% of the electricity produced in the United States comes from nuclear power plants. Traditionally, nuclear power plants, as well as larger coal-fired plants, operate in a baseload manner at or near steady-state for prolonged periods of time. Smaller, more maneuverable plants, such as gas-fired plants, are dispatched to match electricity supply and demand above the capacity of the baseload plants. However, air quality concerns and CO 2 emission standards has made the burning of fossil fuels less desirable, despite the current low cost of natural gas. Wind and solar photovoltaic (PV) power generation are attractive options due to their lack of carbon footprint and falling capital costs. Yet, these renewable energy sources suffer from inherent intermittency. This inherent intermittency can strain electric grids, forcing carbon-based and nuclear sources of energy to operate in a load follow mode. For nuclear reactors, load follow operation can be undesirable due to the associated thermal and mechanical stresses placed on the fuel and other reactor components. Various methods of Thermal Energy Storage (TES) can be coupled to nuclear (or renewable) power sources to help absorb grid variability caused by daily load demand changes and renewable intermittency. Our previous research has shown that coupling a sensible heat TES system to a Small Modular Reactor (SMR) allows the reactor to run at effectively nominal full power during periods of variable electric demand by bypassing steam to the TES system during periods of excess capacity. In this paper we demonstrate that this stored thermal energy can be recovered, allowing the TES system to act as a peaking unit during periods of high electric demand, or used to produce steam for ancillary applications such as desalination. For both applications the reactor is capable of operating continuously at approximately 100% power.
A high current conical C-11 gas target with a well characterized production yield was designed an... more A high current conical C-11 gas target with a well characterized production yield was designed and optimized using multi-physics coupling simulations. Two target prototypes were deployed on an IBA 18/9 cyclotron, and the experimental results were used to benchmark the predictive simulations.
To my advisor, Dr. Mike Doster I give my appreciation. Truly, it is men like him that have made a... more To my advisor, Dr. Mike Doster I give my appreciation. Truly, it is men like him that have made a difference in the course of many lives. Five classes and a thesis later I owe him a great deal of my fascination with Nuclear Engineering and my love of thermal-hydraulics, Monte Carlo techniques and a better appreciation on deterministic transport methods. Without his cultivating efforts my evolution from pond scum to amoeba to small gelatinous multi-cellular creature would not have been possible. It is to him that I owe a fighting chance at becoming worthy of the title of Nuclear Engineer. To Dr. Bourham and Dr. Chu; who both have graciously taken time out of their schedules to read, review and solidify this work. Your thoughts and inputs are appreciated. To my friends and colleagues, I give collective thanks. Without sounding boards for thoughts and ideas or without those times to distract me, this work would not be what it is. I appreciate times come and gone and hope for more times to be as memorable as these. To my parents; thank you. It is because of both you that I am here today. You give me strength and wisdom in ways you cannot know. These pieces of paper are but a beginning. v TABLE OF CONTENTS LIST OF TABLES .
An experimental research program into the loose part damage process identified important mechanis... more An experimental research program into the loose part damage process identified important mechanisms that govern accumulated loose part damage to steam generator tube sheets. Relationships were developed to quantify damage due to single and multiple impacts, including such effects as tube end open diameter reduction and tube end contour deformation. These experimental investigations have led to the development of a computational model for estimating loose part impact damage on steam generator tube ends. Comparisons to experimental data show the loose part damage model to be a good approximation of actual loose part impact damage and provide a convenient and quantitative linkage between loose part impact properties and damage. Impact damage effects are local effects that depend only on the single impacts and impact overlaps in a small region of interest. The damage can be directly related to local impact density. Since in general the local impact density on a steam generator tube sheet is unknown, a model developed to simulate loose part impact distributions as a function of operating conditions is described.
To estimate the range of impact velocities of potential reactor loose parts (LPs) requires inform... more To estimate the range of impact velocities of potential reactor loose parts (LPs) requires information on regional flow velocities, LP mass, and LP drag coefficients. Flow velocities and the mass of potential LPs can generally be bounded and therefore are assumed to be known. In this work, drag coefficients for prototype LP shapes, including objects such as bolts, nuts, pins, and hand tools, were measured in the fluid velocity range typical of reactor coolant systems. Unlike drag coefficients measured for stationary objects, or by moving a body through a stagnant fluid, these experiments are performed on objects moving freely in a turbulent flow stream. In general, the measured drag coefficients for all tested LP shapes are shown to be close to the standard drag coefficient for a sphere, especially in the low-Reynolds-number region. However, significant differences exist in the wake transition region, which indicates that the drag coefficient for a freely moving body in turbulent flow is different from the drag coefficient for a confined body under the same flow conditions or for a body moving in a stagnant fluid.
The one-dimensional drift flux model is widely used in the thermal-hydraulic simulation of nuclea... more The one-dimensional drift flux model is widely used in the thermal-hydraulic simulation of nuclear power systems, particularly in simulator and control system modeling where faster-than-real-time solutions are necessary. During normal implementation, however, this model does not correctly simulate buoyancydriven flows and countercurrent flow of liquid and vapor in vertical, stagnant channels. A technique is introduced that overcomes this limitation without using special component models, modifications of the equations of motion, or modifications in constitutive relations.
Natural circulation is important for the long-term cooling of light water reactors in off-normal ... more Natural circulation is important for the long-term cooling of light water reactors in off-normal conditions, and it is therefore important to understand the numerical behavior of reactor safety codes used to simulate flows under those conditions. While the methods and models in these codes have been studied in some detail, the impact of the weight force term on the numerical behavior has been largely ignored. The dynamic and numerical stability of the one-dimensional, single-phase-flow equations are examined for natural-circulation problems. It is shown that the presence of the weight force in the momentum equation results in a minimum value of the frictional loss coefficient for the equations to be stable. It is further shown that the numerical solution is unstable unless this dynamic stability limit is satisfied. The stability limits developed are verified by numerical solution of the single-phase-flow equations under natural-circulation conditions.
Computer codes based on the six-equation or two-fluid model are widely used in simulating nuclear... more Computer codes based on the six-equation or two-fluid model are widely used in simulating nuclear power systems, particularly in an accident simulation where nonequilibrium two-phase flows can exist and accurate modeling of momentum transfer between phases is important. Here, a standard model for describing time-dependent two-phase flows is the so-called six-equation or two-fluid model, where mass, energy, and momentum equations are considered for each phase. It is well known that the single-pressure form of this model can contain complex characteristics and is therefore ill posed. This ill-posedness has been blamed for numerical instabilities that have at times been observed when finite difference solutions of these equations have been attempted. One method to render the characteristics real is to include viscous terms. The numerical implications of adding viscous terms to the six-equation model are considered, and the potential impact of these implications on the stability of the finite difference solution is evaluated.
Transactions of the American Nuclear Society, 1986
Current efforts are under way to develop and evaluate numerical algorithms for the parallel solut... more Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required.
Numerical solutions involving finite difference representations of the equations governing fluid ... more Numerical solutions involving finite difference representations of the equations governing fluid flow, heat conduction, and diffusion processes (including neutron diffusion) usually consist of solving large sparse matrix equations. These matrix equations can be recast into M smaller coupled matrix equations amenable to solution by using M multiple computer processors operating in parallel. A special form of the fluids equations commonly used in nuclear reactor thermal-hydraulic analysis, i.e., one-dimensional flow in closed loop geometry is emphasized. Parallel algorithms for solving these equations are developed and evaluated in terms of computational speed against conventional solutions on a serial machine. Timing studies are performed to assess the efficiency of these methods and to determine the optimum number of parallel processors for these applications. Algorithmes de traitement en parallele pour resoudre les equations de Navier-Stokes d'apres la methode des differences finies
Drift-flux models can be used to describe two-phase-flow systems when explicit representation of ... more Drift-flux models can be used to describe two-phase-flow systems when explicit representation of the relative phase motion is not required. In these models, relative phase velocity is described by flowregime-dependent, semiempirical models. Numerical stability of the mixture drift-flux equations is examined for different semi-implicit time discretization schemes. Representative flow-regime-dependent drift-flux correlations are considered, and analytic stability limits are derived based on these correlations. The analytic stability limits are verified by numerical experiments run in the vicinity of the predicted stable boundaries. It is shown that the stability limits are strong functions of the time-level specification and functional form chosen for the relative phase velocity. It is also shown that the mixture Courant limit normally associated with these methods is insufficient for ensuring a stable numerical scheme.
Mixture models are commonly used in the simulation of transient two-phase flows as simplification... more Mixture models are commonly used in the simulation of transient two-phase flows as simplifications of six-equation models, with the drift-flux models as a common way to describe relative phase motion. This is particularly true in simulator and control system modeling where solutions that are faster than real time are necessary, and as a means for incorporating thermal-hydraulic feedback into steady-state and transient neutronics calculations. Variations on semi-implicit finite difference schemes are some of the more commonly used temporal discretization schemes. The maximum timestep size associated with these schemes is normally assumed to be limited by stability considerations to the material transport time across any computational cell (Courant limit). In applications requiring solutions that are faster than real time or the calculation of thermal-hydraulic feedback in reactor kinetics codes, time-step sizes that are restricted by the material Courant limit may result in prohibitive run times. A Courant violating scheme is examined for the mixture drift-flux equations, which for rapid transients is at least as fast as classic semi-implicit methods and for slow transients allows timestep sizes many times greater than the material Courant limit.
Computer models w i l l be used t o s imulate the performance o f a number o f TES/heat pump conf... more Computer models w i l l be used t o s imulate the performance o f a number o f TES/heat pump conf igura t ions . Models w i l l be based on e x i s t i n g performance data o f heat pump components, a v a i l ab le b u i l d i n g thermal 1 oad computational procedures, and general ized TES subsystem design. D i f f e r e n t e l e c t r i c i t y r a t e s t ruc tures w i l l be assumed f o r each s i t e . L i f e c y c l e costs f o r each s i t e , con f i gu ra t i on and r a t e s t r u c t u r e w i l l then be computed.
Interest is in developing neutronic and thermal-hydraulic computer programs that execute efficien... more Interest is in developing neutronic and thermal-hydraulic computer programs that execute efficiently on advanced engineering work stations. Engineering work stations are characterized by a 32-bit arithmetic processor, graphics capabilities, and networking capabilities. These attributes allow an engineer to solve substantive problems in a graphical interactive environment with shared resources available via networking. An advanced engineering work station is further characterized
The thermal-hydraulic code FLOC has been developed to investigate the vector and multi-CPU perfor... more The thermal-hydraulic code FLOC has been developed to investigate the vector and multi-CPU performance of advanced computer systems. The FLOC code solves the area-averaged Navier-Stokes equations using a semi-implicit formulation that produces a linear system in terms of the spatial pressure distribution. This code was written on a VAX and transported to a CRAY X-MP, where it was optimized for
A thermal-hydraulics code named FLOC, developed specifically to investigate parallel numerical al... more A thermal-hydraulics code named FLOC, developed specifically to investigate parallel numerical algorithms for solution of the area-averaged Navier-Stokes equations, was originally written to run on a VAX minicomputer and later implemented on a CRAY X-MP. The FLOC code utilizes a semiimplicit formulation to produce a linear system in the spatial pressure distribution at each time step. As transported, the code ran at just over 4 MFLOPs and required 25 CPUs to complete a 10-s pump startup transient for a 72-volume/84-junction two-loop representation of a pressurized water reactor. After restructuring to enhance vectorization by the CRAY vectorizing compiler (version 1.15), the same transient ran at > 23 MFLOPs in < 4 CPUs using fixed time steps. The same simulation allowing variable time steps ran in 0.7 s, more than 10 times faster than real time. The FLOC code consists of eight subroutines, which are called at each time step, and several additional subroutines, which perform i...
For the past several years, a full plant engineering simulation code has been under development i... more For the past several years, a full plant engineering simulation code has been under development in the Nuclear Engineering Department at North Carolina State University to simulate the dynamic response of Pressurized Water Reactor Systems. The software is used in the Department's Reactor Systems course, as well as a number of other undergraduate courses to demonstrate the effectiveness of the plants control and protection systems and illustrate transient systems behavior during normal and off-normal operating conditions. The software has served as the basis of a Simulation Laboratory within the Department with the goal of providing a convenient, interactive platform for the design and analysis of reactor systems.
Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotr... more Introduction Combined thermal and fluid modeling is useful for design and optimization of cyclotron water targets. Previous heat transfer models assumed either a distribution of void under saturation conditions [1] or a static volumetric heat distribution [2]. This work explores the coupling of Monte Carlo radiation transport and Computation Fluid Dynamics (CFD) software in a computational model of the BTI Targetry visualization target [3]. In a batch water target, as the target medium is heated by energy deposition from the proton beam, a non-uniform density distribution develops. Production target operation is ultimately limited by the range thickness of the target under conditions of reduced water density. Since proton range is a function of target density, the system model must include the corresponding change in the volumetric heat distribution. As an initial attempt to couple the radiation transport and fluid dynamics calculations, the scope of this work was limited to subcool...
Approximately 19% of the electricity produced in the United States comes from nuclear power plant... more Approximately 19% of the electricity produced in the United States comes from nuclear power plants. Traditionally, nuclear power plants, as well as larger coal-fired plants, operate in a baseload manner at or near steady-state for prolonged periods of time. Smaller, more maneuverable plants, such as gas-fired plants, are dispatched to match electricity supply and demand above the capacity of the baseload plants. However, air quality concerns and CO 2 emission standards has made the burning of fossil fuels less desirable, despite the current low cost of natural gas. Wind and solar photovoltaic (PV) power generation are attractive options due to their lack of carbon footprint and falling capital costs. Yet, these renewable energy sources suffer from inherent intermittency. This inherent intermittency can strain electric grids, forcing carbon-based and nuclear sources of energy to operate in a load follow mode. For nuclear reactors, load follow operation can be undesirable due to the associated thermal and mechanical stresses placed on the fuel and other reactor components. Various methods of Thermal Energy Storage (TES) can be coupled to nuclear (or renewable) power sources to help absorb grid variability caused by daily load demand changes and renewable intermittency. Our previous research has shown that coupling a sensible heat TES system to a Small Modular Reactor (SMR) allows the reactor to run at effectively nominal full power during periods of variable electric demand by bypassing steam to the TES system during periods of excess capacity. In this paper we demonstrate that this stored thermal energy can be recovered, allowing the TES system to act as a peaking unit during periods of high electric demand, or used to produce steam for ancillary applications such as desalination. For both applications the reactor is capable of operating continuously at approximately 100% power.
A high current conical C-11 gas target with a well characterized production yield was designed an... more A high current conical C-11 gas target with a well characterized production yield was designed and optimized using multi-physics coupling simulations. Two target prototypes were deployed on an IBA 18/9 cyclotron, and the experimental results were used to benchmark the predictive simulations.
To my advisor, Dr. Mike Doster I give my appreciation. Truly, it is men like him that have made a... more To my advisor, Dr. Mike Doster I give my appreciation. Truly, it is men like him that have made a difference in the course of many lives. Five classes and a thesis later I owe him a great deal of my fascination with Nuclear Engineering and my love of thermal-hydraulics, Monte Carlo techniques and a better appreciation on deterministic transport methods. Without his cultivating efforts my evolution from pond scum to amoeba to small gelatinous multi-cellular creature would not have been possible. It is to him that I owe a fighting chance at becoming worthy of the title of Nuclear Engineer. To Dr. Bourham and Dr. Chu; who both have graciously taken time out of their schedules to read, review and solidify this work. Your thoughts and inputs are appreciated. To my friends and colleagues, I give collective thanks. Without sounding boards for thoughts and ideas or without those times to distract me, this work would not be what it is. I appreciate times come and gone and hope for more times to be as memorable as these. To my parents; thank you. It is because of both you that I am here today. You give me strength and wisdom in ways you cannot know. These pieces of paper are but a beginning. v TABLE OF CONTENTS LIST OF TABLES .
An experimental research program into the loose part damage process identified important mechanis... more An experimental research program into the loose part damage process identified important mechanisms that govern accumulated loose part damage to steam generator tube sheets. Relationships were developed to quantify damage due to single and multiple impacts, including such effects as tube end open diameter reduction and tube end contour deformation. These experimental investigations have led to the development of a computational model for estimating loose part impact damage on steam generator tube ends. Comparisons to experimental data show the loose part damage model to be a good approximation of actual loose part impact damage and provide a convenient and quantitative linkage between loose part impact properties and damage. Impact damage effects are local effects that depend only on the single impacts and impact overlaps in a small region of interest. The damage can be directly related to local impact density. Since in general the local impact density on a steam generator tube sheet is unknown, a model developed to simulate loose part impact distributions as a function of operating conditions is described.
To estimate the range of impact velocities of potential reactor loose parts (LPs) requires inform... more To estimate the range of impact velocities of potential reactor loose parts (LPs) requires information on regional flow velocities, LP mass, and LP drag coefficients. Flow velocities and the mass of potential LPs can generally be bounded and therefore are assumed to be known. In this work, drag coefficients for prototype LP shapes, including objects such as bolts, nuts, pins, and hand tools, were measured in the fluid velocity range typical of reactor coolant systems. Unlike drag coefficients measured for stationary objects, or by moving a body through a stagnant fluid, these experiments are performed on objects moving freely in a turbulent flow stream. In general, the measured drag coefficients for all tested LP shapes are shown to be close to the standard drag coefficient for a sphere, especially in the low-Reynolds-number region. However, significant differences exist in the wake transition region, which indicates that the drag coefficient for a freely moving body in turbulent flow is different from the drag coefficient for a confined body under the same flow conditions or for a body moving in a stagnant fluid.
The one-dimensional drift flux model is widely used in the thermal-hydraulic simulation of nuclea... more The one-dimensional drift flux model is widely used in the thermal-hydraulic simulation of nuclear power systems, particularly in simulator and control system modeling where faster-than-real-time solutions are necessary. During normal implementation, however, this model does not correctly simulate buoyancydriven flows and countercurrent flow of liquid and vapor in vertical, stagnant channels. A technique is introduced that overcomes this limitation without using special component models, modifications of the equations of motion, or modifications in constitutive relations.
Natural circulation is important for the long-term cooling of light water reactors in off-normal ... more Natural circulation is important for the long-term cooling of light water reactors in off-normal conditions, and it is therefore important to understand the numerical behavior of reactor safety codes used to simulate flows under those conditions. While the methods and models in these codes have been studied in some detail, the impact of the weight force term on the numerical behavior has been largely ignored. The dynamic and numerical stability of the one-dimensional, single-phase-flow equations are examined for natural-circulation problems. It is shown that the presence of the weight force in the momentum equation results in a minimum value of the frictional loss coefficient for the equations to be stable. It is further shown that the numerical solution is unstable unless this dynamic stability limit is satisfied. The stability limits developed are verified by numerical solution of the single-phase-flow equations under natural-circulation conditions.
Computer codes based on the six-equation or two-fluid model are widely used in simulating nuclear... more Computer codes based on the six-equation or two-fluid model are widely used in simulating nuclear power systems, particularly in an accident simulation where nonequilibrium two-phase flows can exist and accurate modeling of momentum transfer between phases is important. Here, a standard model for describing time-dependent two-phase flows is the so-called six-equation or two-fluid model, where mass, energy, and momentum equations are considered for each phase. It is well known that the single-pressure form of this model can contain complex characteristics and is therefore ill posed. This ill-posedness has been blamed for numerical instabilities that have at times been observed when finite difference solutions of these equations have been attempted. One method to render the characteristics real is to include viscous terms. The numerical implications of adding viscous terms to the six-equation model are considered, and the potential impact of these implications on the stability of the finite difference solution is evaluated.
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