Begell House Inc.
Multiphase Science and Technology
MST
0276-1459
25
2-4
2013
PREFACE: A SPECIAL TRIBUTE TO THE MEMORY OF DR. NOVAK ZUBER
101-102
10.1615/MultScienTechn.v25.i2-4.10
Jean-Marc
Delhaye
Clemson University, Department of Mechanical Engineering, USA
IN REMEMBRANCE OF NOVAK ZUBER
103-105
10.1615/MultScienTechn.v25.i2-4.20
Ivan
Catton
Morin, Martinelli, Gier Memorial Heat Transfer Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, University of California, Los Angeles, USA
NOVAK ZUBER AND THE DRIFT FLUX MODEL
107-112
10.1615/MultScienTechn.v25.i2-4.30
Graham B.
Wallis
Thayer School of Engineering, Dartmouth College, Hanover, NH 03755
HASH(0xabb8bb8)
NOVAK ZUBER AT GEORGIA INSTITUTE OF TECHNOLOGY (1969-1974)
113-115
10.1615/MultScienTechn.v25.i2-4.40
Wolfgang
Wulff
Nonproliferation and National Security Department, Brookhaven National Laboratory; Stony Brook University, P.O. Box 5000, Upton, NY 11973-5000
DELAYED EQUILIBRIUM MODEL (DEM) OF FLASHING CHOKED FLOWS RELEVANT TO LOCA
117-131
10.1615/MultScienTechn.v25.i2-4.50
Yann
Bartosiewicz
Institute of Mechanics, Materials and Civil Engineering (iMMC), Universite Catholique de Louvain (UCL), 1348 Louvain-la-Neuve, Belgium
Jean-Marie
Seynhaeve
Institute of Mechanics, Materials and Civil Engineering (iMMC), Universite Catholique de Louvain (UCL), 1348 Louvain-la-Neuve, Belgium
flashing
choked flows
LOCA
critical conditions
metastable states
thermodynamic non equilibrium
NPP
In the context of nuclear reactor safety, a pipe breach in the primary circuit is the initiator of a loss of coolant accident (LOCA). The calculation of leak rates involving the discharge of water and steam mixtures plays an important role in the modeling of LOCAs for both generation (GEN) II and GEN III reactors, and also for the supercritical water reactor of GEN IV. Indeed, the flow though the breach determines the depressurization rate of the system and the time to core uncover, which in turn are of major concern for when and how different mitigation auxiliary systems will be initiated and efficient. This paper deals with the delayed equilibrium model (DEM), which focuses on thermodynamic non-equilibrium conditions that prevail in the flashing flow process near the critical section. The DEM developed at the University of Louvain is a one-dimensional model for the choked or critical flow rate in steady-state or quasi-steady-state conditions, which deals with the effect of the metastable liquid phase during the flashing process. The DEM has been compared with 500 experimental data. The DEM was recently assessed against the Super-Mobydick and Bethsy experiments done at the Commissariat a L'Energie Atomique during the 1980s.
ONE-DIMENSIONAL TWO-EQUATION TWO-FLUID MODEL STABILITY
133-167
10.1615/MultScienTechn.v25.i2-4.60
Martin
Lopez-de-Bertodano
School of Nuclear Engineering, Purdue University, West Lafayette, Indiana 47907, USA
William
Fullmer
School of Nuclear Engineering, Purdue University, West Lafayette, Indiana 47907, USA
Avinash
Vaidheeswaran
School of Nuclear Engineering, Purdue University, West Lafayette, Indiana 47907, USA
two-phase flow
two-fluid model
shallow water equations
Kelvin-Helmholtz
The one-dimensional incompressible two-fluid model based on physical closures is reduced to simpler two-equation models for horizontal or near-horizontal stratified and vertical bubbly flows. For stratified flow with small density ratio the model may be simplified further to obtain the one-dimensional shallow water theory equations. Characteristic, dispersion, and nonlinear analyses are performed to demonstrate that the models are linearly well-posed and nonlinearly bounded. Linear stability of the two-equation model for horizontal or near-horizontal stratified flow shows that the model is made well-posed by the hydrostatic force for a range of relative velocity surrounding the homogeneous condition. As the relative velocity increases, the model becomes unstable yet well-posed once the kinematic shallow water theory instability occurs, i.e., the viscous KelvinHelmholtz instability. However, unlike shallow water theory, the two-equation two-fluid model becomes ill-posed when the relative velocity reaches the dynamic inviscid KelvinHelmholtz instability, unless higher order modeling is incorporated, i.e., surface tension. Aside from these well-known results a new analytic expression for the kinematic instability is obtained because of the simplified mathematics of the two-equation model. Linear stability of the two-equation model for bubbly flow including the virtual mass and interfacial pressure forces shows that it is well-posed for low void fractions. It is now demonstrated that it becomes unconditionally well-posed when a bubble collision force is incorporated. It is also demonstrated that the two-equation model for bubbly flow becomes kinematically unstable when the shallow water theory stability condition is reached even though the bubbly flow model is more complicated than shallow water theory. Finally, the nonlinear evolution of the kinematic instability is simulated numerically for a case of Stokes bubbly flow. It is shown that the linearly unstable conditions result in a nonlinearly bounded limit cycle. The bounding mechanism is the viscous stress. Well-posedness and boundedness are of practical significance for nuclear reactor safety code verification because they enable convergence of the numerical two-fluid model.
MEASUREMENTS OF THE LOCAL RELATIVE VELOCITY AND THE PROFILE EFFECTS ON PREDICTION OF THE AREA-AVERAGED RELATIVE VELOCITY
169-199
10.1615/MultScienTechn.v25.i2-4.70
Benjamin
Doup
Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA
Xinquan
Zhou
Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA
In Hun
Kim
Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA
Xiaodong
Sun
Nuclear Engineering Program, Department of Mechanical and Aerospace Engineering, The Ohio State University, 201 W 19th Avenue, Columbus, OH 43210, USA
two-phase flow
local relative velocity measurements
four-sensor conductivity probe
particle image velocimetry
Measurements of the local relative velocity in vertical air/water two-phase bubbly, cap-bubbly, and slug flows at 10 and 32 pipe diameters from the inlet are investigated. The measurements were performed conducted in an acrylic vertical pipe with an inner diameter of 50 mm and a height of 3.2 m. A four-sensor conductivity probe was used to measure the local gas-phase velocities and void fractions. The void fraction profiles are presented to illustrate the flow structure. These profiles along with a high-speed imaging system were used to classify the flow regimes. A particle image velocimetry system was employed to measure the local liquid-phase velocities. To perform this measurement, the planar laser-induced fluorescence technique and an image pre-processing scheme were used to separate the liquid-phase information from that of the gas phase. The local experimental data are used to investigate the effects of area averaging and to directly calculate the area-averaged relative velocity and the two-phase distribution parameter of the drift-flux model, and then the results are compared with correlations provided in the literature. In addition, the local axial relative velocity obtained from these local gas- and liquid-phase measurements will be useful in benchmarking interfacial momentum transfer models.
SATURATION BOILING ON MPC: EFFECTS OF THICKNESS, INCLINATION ANGLE, TRANSIENT BUBBLE GROWTH, AND NUCLEATION SITE DENSITY
201-236
10.1615/MultScienTechn.v25.i2-4.80
Mohamed S.
El-Genk
Institute for Space and Nuclear Power Studies; Mechanical Engineering Department; Nuclear Engineering Department, Chemical & Biological Engineering Dept., University of New Mexico, Albuquerque, New Mexico, 87131 USA
Amir F.
Ali
Institute for Space & Nuclear Power Studies, University of New Mexico, Albuquerque, New Mexico, USA; Mechanical Engineering Department, University of New Mexico, Albuquerque, New Mexico, USA
nucleate boiling
micro-porous copper
surface inclination
dielectric liquid
transient bubble growth
departure bubble diameter and detachment frequency
active nucleation site density
Saturation pool boiling experiments of PF-5060 dielectric on micro-porous copper (MPC) near atmospheric pressure (~0.085 MPa) have investigated the effects of the inclination angle (θ) and thickness (δMPC) on the nucleate boiling (NB) heat transfer coefficient (hNB) and critical heat flux (CHF). In the experiments, δMPC varied from 80 to 230 µm and θ varied from 0° (upward facing) to 180° (downward facing). In addition to enhancing hNB, there was no (or a slight) excursion in the surface temperature (<5 K) prior to boiling incipience. Increasing δMPC from 95 to 230 µm increased the CHF from 22 to 26 W/cm2. The highest [maximum nucleate boiling (MNB)] heat transfer coefficient (hMNB) near the end of fully developed NB region occurred at lower superheat than at the CHF. Both hNB and hMNB increased with increasing δMPC, peaking at ~171 µm, and then decreased with a further increase in δMPC. They were highest in the upward-facing orientation. The hMNB value (up to ~7.8 W/cm2· K) decreased slowly with increasing θ to 90°, and then decreased faster to the lowest value at 180°. In the upward-facing orientation hNB was correlated in terms of the applied heat flux (hNB = AqB); coefficient A increased linearly from 0.427 to 1.143 as δMPC increased from 80 to 230 µm, while B increased from 0.522 to a peak of 0.686 at δMPC ~ 162 µm, and then decreased to 0.573 at δMPC = 230 µm. The hNB correlation agreed with the data to within ±12%. Also developed was a correlation for the transient bubble growth on MPC at low heat flux (<0.48 W/cm2 ). This correlation agreed to within ±5% with measurements from footings recorded using a video camera at 210 frames per second. The bubble's departure diameter (Dd = 431 ± 7 µm ) and detachment frequency (fd = 36 ± 2 Hz) in the upward-facing orientation were independent of δMPC. The active nucleation site densities on MPC, based on these values of Dd and fd and the boiling curves in the experiments, ranged from ~725 to 1.07 × 104 sites/cm2.
MODEL OF THE COOLING OF A NUCLEAR REACTOR FUEL ROD
237-248
10.1615/MultScienTechn.v25.i2-4.90
David
Lavicka
New Technology Research Center (NTC), University of West Bohemia, Univerzitni 8, 306 14 Plzen, Czech Republic
Jiri
Polansky
New Technology Research Center (NTC), University of West Bohemia, Univerzitni 8, 306 14 Plzen, Czech Republic
nuclear reactor fuel rod
vertical pipe
spacers
laser anenometry
This paper presents an experimental setup showing some typical phenomena associated with the cooling of a fuel rod inside a nuclear reactor. The fuel rod model allows the general public to observe phenomena related to fluid mechanics and heat transfer. Safety and operational reasons usually prevent these phenomena from being observed in real-life equipment. The most interesting and important phenomena are boiling crisis and transient heat transfer in two-phase flow.
INVESTIGATION OF subscriptCOOLEDWATER DISCHARGE THROUGH SIMULATED STEAM GENERATOR TUBE CRACKS
249-285
10.1615/MultScienTechn.v25.i2-4.100
Shripad
Revankar
Purdue University
Brian
Wolf
NuScale Power, 1100 NE Circle Blvd., Suite 350, Corvallis, Oregon 97330, USA
Jovica R.
Riznic
Canadian Nuclear Safety Commission, 280 Slater Street, P.O. Box 1046, Station B, Ottawa, Ontario, Canada, K1P 5S9
flashing flow
choking flow
steam generator tube cracks
experiments
homogeneous equilibrium model
homogeneous non-equilibrium model
channel length effects
The work presented here describes an investigation into the choked flow of initially subscriptcooled water through simulated steam generator tube cracks at pressures up to 7 MPa. The study of such flow is relevant to the prediction of leak flow rates from a nuclear reactor primary side to secondary side through cracks in steam generator tubes. A facility was designed to measure the leak rates and experiments were conducted on choking flow for various vessel pressures and subscriptcooling. Measurements were done on subscriptcooled flashing flow rate through well-defined simulated crack geometries with ratio of channel length to hydraulic diameter between 4.5 and 7. Both homogeneous equilibrium and non-equilibrium mechanistic models were developed to predict two-phase choking flow through slits. Experimental results from data found in literature as well as the data collected in this work are compared with predictions from presented models. It is found that the homogeneous equilibrium model underpredicts choked flow rates of subscriptcooled water through slits and artificial steam generator tube cracks. Additional modeling of thermal non-equilibrium improves the predictability of choking mass flux for the homogeneous model.
COMPUTATIONAL FLUID DYNAMICS SIMULATION OF SINGLE BUBBLE DYNAMICS IN CONVECTIVE BOILING FLOWS
287-309
10.1615/MultScienTechn.v25.i2-4.110
Yohei
Sato
Nuclear Energy and Safety, Paul Scherrer Institute, Villigen, 5232, Switzerland
Sreeyuth
Lal
Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland
Bojan
Niceno
Laboratory for Thermal Hydraulics, Department of Nuclear Energy and Safety, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
convective boiling
nucleate boiling
computational fluid dynamics (CFD)
interface tracking method
A sharp-interface phase-change model, which was developed in the framework of direct numerical simulation, has been extended to turbulent flows by introducing the Smagorinsky subscript-grid-scale model and applied to simulations of convective nucleate boiling flows. The developed model is validated against the experiments of convective boiling flows in the horizontal and vertical flow directions. Although the bubbles were successively released from the wall in the experiment, the simulations take into account only single bubble growth, and several assumptions are used for the initial and boundary conditions to complement the limited measured data. Thus, the comparison between the simulation and the experiment is not considered as a rigorous validation. In spite of this, the computed bubble lift-off diameter and lift-off time show generally good agreement with the experiments under the given conditions, and the applicability of the developed method to the simulation of convective boiling flows is demonstrated. Compared to a previous computational fluid dynamics study, our method cannot show improvement in terms of accuracy; however, the effects of turbulence are taken into account in our model, which should be essential for convective boiling flows with higher Reynolds numbers. The discrepancy between the measurement and simulation results is mainly caused by the steady-state assumption used in the micro-region model.
EFFICIENT HYDRAULIC AND THERMAL ANALYSIS OF HEAT SINKS USING VOLUME AVERAGING THEORY AND GALERKIN METHODS
311-338
10.1615/MultScienTechn.v25.i2-4.120
Krsto
Sbutega
University of California, Los Angeles, UCLA MAE, Box 951597, 48-121 E4, Los Angeles, California 90095-1597, USA
Ivan
Catton
Morin, Martinelli, Gier Memorial Heat Transfer Laboratory, Department of Mechanical and Aerospace Engineering, School of Engineering and Applied Science, University of California, Los Angeles, USA
Galerkin method
volume averaging theory
pin-fin heat sink
micro-channel heat sink
Air- and water-cooled heat sinks are still the most common heat rejection devices in electronics, making their geometric optimization a key issue in thermal management. Because of the complex geometry, the use of finite-difference, finite-volume, or finite-element methods for the solution of the governing equations becomes computationally expensive. In this work, volume averaging theory is
applied to a general heat sink with periodic geometry to obtain a physically accurate, but geometrically simplified, system model. The governing energy and momentum equations are averaged over a representative elementary volume, and the result is a set of integro-partial differential equations. Closure coefficients are introduced, and their values are obtained from data available in the literature.
The result of this process is a system of closed partial differential equations, defined on a simple geometry,
which can be solved to obtain average velocities and temperatures in the system. The intrinsic smoothness of the solution and the simplified geometry allow the use of a modified Fourier−Galerkin Method for efficient solutions to the set of differential equations. Modified Fourier series are chosen as the basis functions because they satisfy the boundary conditions a priori and lead to a sparse system of linear equations for the coefficients. The validity of the method is tested by applying it to model the hydraulic and thermal behavior of an air-cooled pin-fin and a water-cooled micro-channel heat sink. The convergence was found to be O(N-3.443), while the runtime was ~0.25 s for N = 56. The numerical results were validated against the experimental results, and the agreement was excellent with an average error of ~4% and a maximum error of ~5%.
CONTENTS, VOLUME 25
339
10.1615/MultScienTechn.v25.i2-4.130
INDEX, VOLUME 25
340-341
10.1615/MultScienTechn.v25.i2-4.140