Steady Propagation of the Vaporization Front in Metastable Liquid

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
S. P. Aktershev ◽  
V. V. Ovchinnikov
Keyword(s):  
Experimental Data ◽  
Vapor Bubble ◽  
Nuclear Reactor ◽  
Threshold Value ◽  
Metastable Liquid ◽  
Interface Motion ◽  
Wide Range ◽  
Vaporization Front ◽  
Velocity Of Propagation ◽  
Steady Propagation

The boiling up of a metastable liquid when the vaporization fronts appear is considered theoretically and experimentally. Boiling up occurs usually on the surface of a heater. At the first stage, the growth of a spherical vapor bubble is observed. If the temperature of liquid exceeds the threshold value, the vaporization fronts develop near to the line of contact of a vapor bubble and heater. Fronts of vaporization extend along a heater with constant speed. It is a direct transition from one phase convection to film boiling. Such scenario of crisis of a convective heat transfer is also possible in the nuclear reactor equipment. The model of steady propagation of the vaporization front is developed. The temperature and velocity of propagation of the interface are determined from the balance equations for the mass, momentum, and energy in the neighborhood of the vaporization front and the condition of stability of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The velocity of propagation of the vaporization front also has a threshold value. The calculated velocity of the interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid. The developed model adequately describes the experimental data for various substances in a wide range of temperature of an overheated fluid. In this model, the steady propagation of the vaporization front is possible only if the temperature of a metastable liquid exceeds some threshold value. The velocity of the vaporization front also has a threshold value.

Steady Propagation of the Vaporization Front in Metastable Liquid

2009 ◽  
Author(s):  
Sergey Aktershev ◽  
Valeryi Ovchinnikov
Keyword(s):  
Vapor Bubble ◽  
Nuclear Reactor ◽  
Threshold Value ◽  
Direct Transition ◽  
Metastable Liquid ◽  
Interface Motion ◽  
Vaporization Front ◽  
Velocity Of Propagation ◽  
Steady Propagation ◽  
Calculated Velocity

The boiling up of a metastable liquid when the vaporization fronts appear is considered by theoretically and experimentally. Boiling up occurs as usually on a surface of a heater. At the first stage the growth of a spherical vapor bubble is observed. If the temperature of liquid exceeds threshold value, the vaporization fronts develop near to line of contact of a vapor bubble and heater. Fronts of vaporization extend along a heater with constant speed. It is direct transition from one-phase convection to a film boiling. Such scenario of crisis of a convective heat transfer also is possible in the nuclear reactor equipment. The model of steady propagation of the vaporization front is developed. The temperature and velocity of propagation of the interface are determined from the balance equations for the mass, momentum, and energy in the neighborhood of the vaporization front and the condition of stability of motion of the interface. It is shown that a solution of these equations exists only if the liquid is heated above a threshold value. The velocity of propagation of vaporization front has threshold value also. The calculated velocity of interface motion and the threshold value of temperature are in reasonable agreement with available experimental data for various liquids within wide ranges of saturation pressures and temperatures of the overheated liquid.

Effects of Various Parameters on Supercritical-Pressure Heat Transfer and Limits for Heat Transfer Correlations Obtained in Vertical Bare Tubes

2017 ◽  
Author(s):  
Hakim Maloufi ◽  
Hanqing Xie ◽  
Andrew Zopf ◽  
William Anderson ◽  
Christian Langevin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Nuclear Power ◽  
Nuclear Reactor ◽  
Heat Fluxes ◽  
Operating Conditions ◽  
Transfer Coefficients ◽  
Wide Range ◽  
Heat Transfer Correlations ◽  
Bare Tube

Currently, there is a number of Generation-IV SuperCritical Water-cooled nuclear-Reactor (SCWR) concepts under development worldwide. These high temperature and pressure reactors will have significantly higher operating parameters compared to those of current water-cooled nuclear-power reactors (i.e., “steam” pressures of about 25 MPa and “steam” outlet temperatures up to 625 °C). Additionally, SCWRs will have a simplified flow circuit in which steam generators, steam dryers, steam separators, etc. will be eliminated, as the steam will be flowing directly to a steam turbine. In support of developing SCWRs studies are being conducted on heat transfer at SuperCritical Pressures (SCPs). Currently, there are very few experimental datasets for heat transfer at SCPs in power-reactor fuel bundles to a coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations developed with bare-tube data can be used as a conservative approach. Selected empirical heat-transfer correlations, based on experimentally obtained datasets, have been put forward to calculate Heat Transfer Coefficients (HTCs) in forced convective in various fluids, including water at SCPs. The Mokry et al. correlation (2011) has shown a good fit for experimental data at supercritical conditions within a wide range of operating conditions in Normal and Improved Heat-Transfer (NHT and IHT) regimes. However, it is known that a Deteriorated Heat-Transfer (DHT) regime appears in bare tubes earlier than that in bundle flow geometries. Therefore, it is important to know if bare-tube heat-transfer correlations for SCW can predict HTCs at heat fluxes beyond those defined as starting of DHT regime in bare tubes. The Mokry et al. (2011) correlation fits the best SCW experimental data for HTCs and inner wall temperature for bare tubes at SCPs within the NHT and IHT regimes. However, this correlation might have problems with convergence of iterations at heat fluxes above 1000 kW/m2.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

Comparative analysis and verification of engineering methods of shallow cracks effect for fracture toughness prediction for reactor pressure vessels

2020 ◽  
pp. 140-165
Author(s):  
V. I. Kostylev ◽  
B. Z. Margolin
Keyword(s):  
Experimental Data ◽  
Fracture Toughness ◽  
Comparative Analysis ◽  
Nuclear Reactor ◽  
Probabilistic Approach ◽  
Pressure Vessels ◽  
Local Methods ◽  
European Method ◽  
Shallow Crack ◽  
Reactor Pressure

The main features of shallow cracks fracture are considered, and a brief analysis of methods allowing to predict the temperature dependence of the fracture toughness KJC (T) for specimens with shallow cracks is given. These methods include DA-method, (JQ)-method, (J-T)-method, “local methods” with its multiparameter probabilistic approach, GP method uses power approach, and also two engineering methods – RMSC (Russian Method for Shallow Crack) and EMSC (European Method for Shallow Crack). On the basis of 13 sets of experimental data for national and foreign steels, a detailed verification and comparative analysis of these two engineering methods were carried out on the materials of the VVER and PWR nuclear reactor vessels considering the effect of shallow cracks.

scholarly journals Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 968-980
Author(s):  
Xueping Du ◽  
Zhijie Chen ◽  
Qi Meng ◽  
Yang Song
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Correlation Equation ◽  
Tube Heat Exchanger ◽  
Flow Friction ◽  
Air Inlet ◽  
Comparison Results ◽  
Wide Range ◽  
Oval Tube

Abstract A high accuracy of experimental correlations on the heat transfer and flow friction is always expected to calculate the unknown cases according to the limited experimental data from a heat exchanger experiment. However, certain errors will occur during the data processing by the traditional methods to obtain the experimental correlations for the heat transfer and friction. A dimensionless experimental correlation equation including angles is proposed to make the correlation have a wide range of applicability. Then, the artificial neural networks (ANNs) are used to predict the heat transfer and flow friction performances of a finned oval-tube heat exchanger under four different air inlet angles with limited experimental data. The comparison results of ANN prediction with experimental correlations show that the errors from the ANN prediction are smaller than those from the classical correlations. The data of the four air inlet angles fitted separately have higher precisions than those fitted together. It is demonstrated that the ANN approach is more useful than experimental correlations to predict the heat transfer and flow resistance characteristics for unknown cases of heat exchangers. The results can provide theoretical support for the application of the ANN used in the finned oval-tube heat exchanger performance prediction.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

The Petrogenetic Model, an Extension of Bowen's Petrogenetic Grid

1962 ◽  
Vol 99 (6) ◽  
pp. 558-569 ◽  
Author(s):  
Peter J. Wyllie
Keyword(s):  
Experimental Data ◽  
Constant Pressure ◽  
Three Dimensional ◽  
Pore Fluid ◽  
Fluid Composition ◽  
Solid Reaction ◽  
Petrogenetic Model ◽  
Wide Range ◽  
Opposite Face ◽  
Reaction Surfaces

AbstractBowen's petrogenetic grid is a PT projection containing univariant curves for decarbonation, dehydration, and solid-solid reactions, with vapour pressure (Pf) equal to total pressure (Ps). Analysis of experimental data in the system MgO–CO2–H2O leads to an expansion of this grid. Three of the important variables in metamorphism when Pf = Ps are P, T, and variation of the pore fluid composition between H2O and CO2. These can be illustrated in a three-dimensional petrogenetic model; one face is a PT plane for reactions occurring with pure H2O, and the opposite face is a similar plane for reactions with pure CO2; these are separated by an axis for pore fluid composition varying between H2O and CO2. Superposition of the PT faces of the model provides the petrogenetic grid. The reactions within the model are represented by divariant surfaces, which may meet along univariant lines. For dissociation reactions, the surfaces curve towards lower temperatures as the proportion of non-reacting volatile increases, and solid-solid reaction surfaces are parallel to the vapour composition axis and perpendicular to the PT axes. The relative temperatures of reactions and the lines of intersections of the surfaces can be illustrated in isobaric sections. Isobaric sections are used to illustrate reactions proceeding at constant pressure with (1) pore fluid composition remaining constant during the reaction, with temperature increasing (2) pore fluid composition changing during the reaction, with temperature increasing, and (3) pore fluid changing composition at constant temperature. The petrogenetic model provides a convenient framework for a wide range of experimental data.

Effects of Multiple Impacts and Size Distribution of Particles on Erosion Predictions Using CFD

2007 ◽  
Author(s):  
Yongli Zhang ◽  
Brenton S. McLaury ◽  
Siamack A. Shirzai
Keyword(s):  
Experimental Data ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Target Material ◽  
Average Particle ◽  
Multiple Impacts ◽  
Cfd Simulations ◽  
Erosion Damage ◽  
Wide Range

Erosion equations are usually obtained from experiments by impacting solid particles entrained in a gas or liquid on a target material. The erosion equations are utilized in CFD (Computational Fluid Dynamics) models to predict erosion damage caused by solid particle impingements. Many erosion equations are provided in terms of an erosion ratio. By definition, the erosion ratio is the mass loss of target material divided by the mass of impacting particles. The mass of impacting particles is the summation of (particle mass × number of impacts) of each particle. In erosion experiments conducted to determine erosion equations, some particles may impact the target wall many times and some other particles may not impact the target at all. Therefore, the experimental data may not reflect the actual erosion ratio because the mass of the sand that is used to run the experiments is assumed to be the mass of the impacting particles. CFD and particle trajectory simulations are applied in the present work to study effects of multiple impacts on developing erosion ratio equations. The erosion equation as well as the CFD-based erosion modeling procedure is validated against a variety of experimental data. The results show that the effect of multiple impacts is negligible in air cases. In water cases, however, this effect needs to be accounted for especially for small particles. This makes it impractical to develop erosion ratio equations from experimental data obtained for tests with sand in water or dense gases. Many factors affecting erosion damage are accounted for in various erosion equations. In addition to some well-studied parameters such as particle impacting speed and impacting angle, particle size also plays a significant role in the erosion process. An average particle size is usually used in analyzing experimental data or estimating erosion damage cases of practical interest. In petroleum production applications, however, the size of sand particles that are entrained in produced fluids can vary over a fairly broad range. CFD simulations are also performed to study the effect of particle size distribution. In CFD simulations, particle sizes are normally distributed with the mean equaling the average size of interest and the standard deviation varying over a wide range. Based on CFD simulations, an equation is developed and can be applied to account for the effect of the particle size distribution on erosion prediction for gases and liquids.

Fuel Droplet Evaporation in a Supercritical Environment

2002 ◽  
Vol 124 (4) ◽  
pp. 762-770 ◽  
Author(s):  
G. S. Zhu ◽  
S. K. Aggarwal
Keyword(s):  
Experimental Data ◽  
Phase Equilibrium ◽  
Ambient Pressure ◽  
Droplet Surface ◽  
Fuel Vapor ◽  
Phase Solubility ◽  
Liquid Density ◽  
Ambient Temperatures ◽  
Droplet Vaporization ◽  
Wide Range

This paper reports a numerical investigation of the transcritical droplet vaporization phenomena. The simulation is based on the time-dependent conservation equations for liquid and gas phases, pressure-dependent variable thermophysical properties, and a detailed treatment of liquid-vapor phase equilibrium at the droplet surface. The numerical solution of the two-phase equations employs an arbitrary Eulerian-Lagrangian, explicit-implicit method with a dynamically adaptive mesh. Three different equations of state (EOS), namely the Redlich-Kwong (RK), the Peng-Robinson (PR), and Soave-Redlich-Kwong (SRK) EOS, are employed to represent phase equilibrium at the droplet surface. In addition, two different methods are used to determine the liquid density. Results indicate that the predictions of RK-EOS are significantly different from those obtained by using the RK-EOS and SRK-EOS. For the phase-equilibrium of n-heptane-nitrogen system, the RK-EOS predicts higher liquid-phase solubility of nitrogen, higher fuel vapor concentration, lower critical-mixing-state temperature, and lower enthalpy of vaporization. As a consequence, it significantly overpredicts droplet vaporization rates, and underpredicts droplet lifetimes compared to those predicted by PR and SRK-EOS. In contrast, predictions using the PR-EOS and SRK-EOS show excellent agreement with each other and with experimental data over a wide range of conditions. A detailed investigation of the transcritical droplet vaporization phenomena indicates that at low to moderate ambient temperatures, the droplet lifetime first increases and then decreases as the ambient pressure is increased. At high ambient temperatures, however, the droplet lifetime decreases monotonically with pressure. This behavior is in accord with the reported experimental data.

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