Condensation Regime Research Articles

Numerical modelling of low-Reynolds number direct contact condensation in a suppression pool test facility

In the safety pressure suppression pool systems of Boiling Water Reactors (BWRs), the condensation rate has to be maintained high enough in order to fulfill their safety function. A major part of this condensation occurs as direct contact condensation (DCC), which governs different modes varying from vigorous chugging of collapsing bubbles to mild condensation on almost flat steam–water interface. This paper discusses the Computational Fluid Dynamics (CFD) simulations of the latter, low-Reynolds number weak condensation regime. The numerical simulations were performed with two CFD codes, NEPTUNE_CFD and OpenFOAM, in which the DCC phenomenon was modelled by using the Eulerian two-fluid approach of interpenetrating continua without interfacial tracking. The interfacial heat transfer between steam and water was modelled by using the DCC models based on the surface renewal and the surface divergence theories. Flow turbulence was solved by employing the standard k–∊ turbulence model. The CFD results of this study were validated against the test results of the POOLEX facility of Lappeenranta University of Technology. In the reference test STB-31, the condensation phenomena were limited to only occur on a stable steam–water interface by very low steam mass flux applied and thermal insulation of the blowdown pipe. The simulation results demonstrated that the surface divergence model predicted the condensation phenomena quite accurately both qualitatively and quantitatively while the surface renewal model overestimated it strongly.

Sessile drops: spreading versus evaporation–condensation

The equations that govern the dynamics of the liquid–vapor interface and contact line of a sessile drop in the spreading and evaporation–condensation regimes are derived. During spreading, the liquid–vapor interface and contact line convect with the liquid and are therefore material. In contrast, when evaporation or condensation occurs, the liquid–vapor interface and contact line migrate relative to the liquid and are therefore nonmaterial. For spreading, the evolution equations consist of kinematical constraints on the normal velocities of the liquid–vapor interface and contact line along with the normal and tangential components of the constitutively augmented standard force balances on the liquid–vapor interface and along the contact line. The tangential components of the standard force balances on the liquid–vapor interface and at the contact line, being solely dissipative, are automatically satisfied at equilibrium. The normal component of the standard force balance on the liquid–vapor interface reduces to the Young–Laplace equation, whereas its counterpart along the contact line simplifies to the generalization, accounting for line energy, of the Young equation mentioned by Gibbs. In the presence of evaporation or condensation, the kinematical constraints are no longer valid. Their absence is compensated for by the normal components of the configurational force balances on the liquid–vapor interface and along the contact line. Hence, away from equilibrium and in the presence of dissipation, a complete description of the liquid–vapor interface and contact line of a volatile drop involves the normal and tangential components of the standard force balances along with the normal components of the configurational force balances. At equilibrium, the normal component of the configurational force balance on the liquid–vapor interface simplifies to the condition for chemical equilibrium requiring the continuity of the chemical potential, whereas its counterpart along the contact line, being entirely dissipative, holds trivially. Comparison with recently proposed kinetic laws for the liquid–vapor interface and contact line of a drop is provided.

Helium and Hydrogen Adsorbed on Spheres and Cylinders

We examine the metastable and unstable regimes of condensation of superfluid helium and parahydrogen on spheres and cylinders at finite temperatures, employing finite range density functionals. The goal is to compare calculations of sizes and spreads of films at the onset of metastability and of instability with the predictions of a simple phenomenological model that contemplates the curvature of the substrate. We have focused on two cases, helium on nanospheres and nanocylinders of different materials, and hydrogen on fullerenes. We are able to locate the onset of metastability and of spinodal instability in the adsorption isotherms of every sample and to extract the width of the condensed fluid. It is shown that the predictions of the so-called simple model agree surprisingly well with the more elaborate calculations.

CFD simulation and pattern recognition analysis of the chugging condensation regime

The chugging direct contact condensation mode in BWR suppression pools is challenging to be analysed either with experiments or numerical simulations. The POOLEX suppression pool test STB-28 of Lappeenranta University of Technology was simulated by using Eulerian-Eulerian 2D-axisymmetric approach of the compressible flow NEPTUNE_CFD software by applying the model of Hughes and Duffey (1991) for interfacial heat transfer between vapour and liquid. As the condensation rate could not be measured experimentally, a pattern recognition algorithm was employed in order to reveal information of the bubble size and the chugging frequency during the chugging condensation mode. With the help of that data it was possible to compare test and simulation results. The simulation results were promising; the bubble size and chugging frequency increased as the pool water heated up, and the results were in the correct range compared to the tests. Simulated chugging mimicked notably well the chugging observed in the tests. It would be possible to improve the accuracy of these results with modest efforts by employing multiple cameras in the tests and by conducting 3D simulations.

Approach and Development of Effective Models for Simulation of Thermal Stratification and Mixing Induced by Steam Injection into a Large Pool of Water

Steam venting and condensation in a large pool of water can lead to either thermal stratification or thermal mixing. In a pressure suppression pool (PSP) of a boiling water reactor (BWR), consistent thermal mixing maximizes the capacity of the pool while the development of thermal stratification can reduce the steam condensation capacity of the pool which in turn can lead to pressure increase in the containment and thereafter the consequences can be severe. Advanced modeling and simulation of direct contact condensation in large systems remain a challenge as evident in commercial and research codes mainly due to small time-steps necessary to resolve contact condensation in long transients. In this work, effective models, namely, the effective heat source (EHS) and effective momentum source (EMS) models, are proposed to model and simulate thermal stratification and mixing during a steam injection into a large pool of water. Specifically, the EHS/EMS models are developed for steam injection through a single vertical pipe submerged in a pool under two condensation regimes: complete condensation inside the pipe and chugging. These models are computationally efficient since small scale behaviors are not resolved but their integral effect on the large scale flow structure in the pool is taken into account.

Experimental investigation of the condensation of R134a and R404A refrigerants in a long, water-cooled, serpentine coils

The subject of the present analysis is the condensation of the environmentally friendly refrigerants R134a and R404A in long, serpentine pipe coils, for Lc/d>800–1000, where Lc is the total length of the coiled pipe, and d is its internal diameter. During condensation in a coiled-pipe condenser, heat exchange occurs in three regimes, i.e., the superheat removal regimes, the two-phase condensation regimes and the condensate subcooling regimes. The length L of the two-phase area significantly affects the values of the average heat transfer coefficient α and the flow resistance (Δp/L) in this area. On the basis of experimental investigations of the condensation process in a long, water-cooled serpentine coil with five pipe coils of differing dimensions, it was established that the condensation mechanism in a long coil pipe differs substantially from that in a horizontal pipe. New experimental correlations were developed to calculate the average heat transfer coefficient and flow resistance in the two-phase area. In these correlations, the dimensions of the two-phase area are characterized by the geometric index L/d. The correlations developed in this study may be useful in the design of water-cooled serpentine-coil condensers.

Experimental study on direct contact condensation of stable steam jet in water flow in a vertical pipe

Direct contact condensation is widely used in industrial applications due to its highly efficient heat and mass transfer. Many experimental and theoretical works have been performed on steam jet condensation in stagnant water in pool. However, the condensation of steam jet in water flow in pipes is not yet fully understood. Here, experiments are performed to study the direct contact condensation of stable steam jet in water flow in a vertical pipe. By using high speed camera and mobile thermocouple probe, we investigate condensation characteristics including the plume shape, plume length, temperature distribution, average heat transfer coefficient, and average Nusselt number. Five different plume shapes (hemispherical, conical, ellipsoidal, cylinder, and divergent) are identified visually, and their distribution is described in a three-dimensional condensation regime diagram based on steam mass flux, water temperature, and Reynolds number of water flow. The dimensionless plume length and average heat transfer coefficient are found to be within the range of 0.29–4.64 and 0.34–11.36MW/m2K, respectively. Besides, empirical correlations are obtained for the dimensionless plume length, average heat transfer coefficient, and average Nusselt number as a function of three dimensionless parameters, i.e., dimensionless steam mass flux, condensation driving potential, and Reynolds number of water flow. The dimensionless radial temperature decreases exponentially from the center to the pipe wall and shows good self-similarity.

Bose-Einstein condensation of photons in an ideal atomic gas

We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine solutions of these equations in the case of high temperatures, when the atomic components of the system can be considered as nondegenerated ideal gases of atoms, and the photonic component can form a state with the Bose condensate. Transcendental equation for transition temperature and expression for the density of condensed photons in the considered system are derived. We also obtain analytical solutions of the equation for the critical temperature in a number of particular cases. The existence of two regimes of Bose condensation of photons, which differ significantly in nature of transition temperature dependence on the total density of photons pumped into the system, is revealed. In one case, this dependence is a traditional fractional-power law, and in another one it is the logarithmic law. Applying numerical methods, we determine boundaries of existence and implementation conditions for different regimes of condensation depending on the physical parameters of the system under study. We also show that for a large range of physical systems that are in equilibrium with photons (from ultracold gases of alkali metals to certain types of ideal plasma), the condensation of photons should occur according to the logarithmic regime.

Heavy solitons in a fermionic superfluid

Solitons-solitary waves that maintain their shape as they propagate-occur as water waves in narrow canals, as light pulses in optical fibres and as quantum mechanical matter waves in superfluids and superconductors. Their highly nonlinear and localized nature makes them very sensitive probes of the medium in which they propagate. Here we create long-lived solitons in a strongly interacting superfluid of fermionic atoms and directly observe their motion. As the interactions are tuned from the regime of Bose-Einstein condensation of tightly bound molecules towards the Bardeen-Cooper-Schrieffer limit of long-range Cooper pairs, the solitons' effective mass increases markedly, to more than 200 times their bare mass, signalling strong quantum fluctuations. This mass enhancement is more than 50 times larger than the theoretically predicted value. Our work provides a benchmark for theories of non-equilibrium dynamics of strongly interacting fermions.

Microporous Polymer Networks (MPNs) Made in Metal-Free Regimes: Systematic Optimization of a Synthetic Protocol toward N-Arylcarbazole-Based MPNs.

Acidic self-condensation of 2,7-bis(N-carbazolyl)-9-fluorenone 1 produces microporous polymer networks (MPNs) with high Brunauer-Emmett-Teller (BET) surface areas of up to 2250 m2/g and hydrogen storage capacities of up to 1.7% (at 1 bar) in a fully metal-free condensation regime.

Tunneling manipulation of superfluid Fermi gas in the adiabatic condition

In the adiabatic limit, we study Rosen–Zener transition of superfluid Fermi gas in a double well potential. We find that s-wave scattering length of the system can affect the quantum transition dramatically. At certain regime the complete population transfer between two wells is observed. On the contrary, the quantum transition could be completely blocked in other regime. We have derived analytical expressions for the transition probability. We also find that, in the adiabatic limit, the population difference between two modes always oscillates around its corresponding fixed point during Rosen–Zener transition process. The difference between population imbalance and the corresponding fixed point decreases with the adiabatic condition becomes stronger. The numerical simulation show a power law relation between them. It is verified by the Rosen–Zener transition for superfluid Fermi gas in the limited cases of both deep Bose-Einstein condensate regime and unitarity regime.

Effects of altitude and climate in determining elevational plant species richness patterns: A case study from Los Tuxtlas, Mexico

Altitudinal changes of composition and richness of montane plant assemblages are complex, depending on the taxonomic group and gradient conditions, with different factors involved that are directly altitude-dependent (e.g., temperatures, air pressure) and altitude-independent (e.g., precipitation, cloud cover, area). In order to assess the relative impacts of temperature, precipitation, air humidity, and area of altitudinal belts on plant diversity, we analyzed diversity patterns of five species-rich groups, mostly herbaceous plants, in 74 forest plots along three climatically contrasting elevational transects from humid tropical lowland vegetation up to cloud forests at Los Tuxtlas, Mexico. We recorded 278 plant species, with ferns being the most species-rich group followed by orchids, bromeliads, aroids, and piperoids. The most striking results were the contrasting patterns and model results for terrestrial and epiphytic taxa. Whereas the richness of all terrestrial species taken together did not change significantly with elevation, vascular epiphytes showed increasing species numbers with altitude. However, a number of individual terrestrial taxa showed also significant elevation-related changes: aroids showed a marked decline with hight, orchids and piperoids increased, and ferns displayed a hump-shaped pattern with highest richness in mid-altitudes. Among the epiphytes, aroids declined while most other groups increased with altitude. This distinction is relevant for projections of responses of plant communities to climate change, which will lead to increased temperatures and to changing precipitation and cloud condensation regimes and thus will likely affect terrestrial and epiphytic species in different ways.

Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum MonteCarlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

In situ SAXS investigation of dibromomethane adsorption in ordered mesoporous silica

A SAXS/WAXS apparatus with the aid of a specially designed sample cell capable for performing both SAXS and WAXS experiments was used for adsorption studies in nanoporous materials. The applicability of the instrument for structural investigations and its ability for adsorption experiments because of the advanced sample environment were demonstrated by carrying out in situ SAXS measurements during gas physisorption. SAXS profiles of ordered mesoporous silica were measured at selected equilibrium points alongside a dibromomethane (CH2Br2) adsorption isotherm at 293 K. SBA-15 was the adsorbent of choice because it consists of a regular 2D hexagonal array of cylindrical mesopores that gives rise to Bragg reflections in the small-angle regime. CH2Br2 was selected as a contrast-matching fluid because it has almost the same electron density as silica. We obtained high-quality data comparable to those resulting from experiments performed in synchrotron light sources which produce intense beams of x-rays and support advanced instrumentation for high-resolution diffraction and SAXS studies. The Bragg peaks of the pore lattice are clearly visible for the evacuated sample and at the early stages of the adsorption process. The intensity decrease and the elimination of the Bragg peaks for the saturated sample suggest that an almost perfect contrast matching was achieved. A model has been used for monitoring the fluid condensation and evaporation regime in SBA-15 by taking into account both the Bragg scattering and the diffuse scattering for spatially random pore filling. The results show the absence of spatial correlations between filled pores suggesting random pore filling.

Two-Phase Flow and Heat Transfer during Steam Condensation in a Converging Microchannel with Different Convergence Angles

The present study experimentally investigates the effect of convergence angle of microchannel on two-phase flow and heat transfer during steam condensation. Three condensation regimes, from the inlet to the outlet, are identified: mist/annular flow, injection flow, and slug-bubbly flow. Flow pattern maps are constructed using superficial vapor and liquid velocities as the coordinates, wherein relatively distinct boundaries between the flow patterns can be identified. The experimental results show that the condensation heat flux increases with an increase in the convergence angle and/or the steam mass flux at a given coolant flow ratebut decreases with an increase in the coolant flow rate at a given steam mass flux. The results further demonstrate that the local condensation heat transfer coefficient in the mist/annular flow region is much higher than that in other condensation regimes. Moreover, the local condensation heat transfer coefficient in the mist/annular flow and injection flow region decreases with an increase in the convergence angle.

Strong binding and shrinkage of single and double <span style="text-decoration: overline;"><i>K</i></span> nuclear systems (<i>K</i><sup>−</sup><i>pp</i>, <i>K</i><sup>−</sup><i>ppn</i>, <i>K</i><sup>−</sup><i>K</i><sup>−</sup><i>p</i> and <i>K</i><sup>−</sup><i>K</i><sup>−</sup><i>pp</i>) predicted by Faddeev-Yakubovsky calculations

Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K−pp, K−ppn, K−K−p and K−K−pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K−-K− and the K−-nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the interaction, were found to increase rapidly with the interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c2 for K−p, the following ground-state binding energies together with the wave functions were obtained: 51.5 MeV (K−pp), 69 MeV (K−ppn), 30.4 MeV (K−K−p) and 93 MeV (K−K−pp), which are in good agreement with previous results of variational calculation based on the Akaishi-Yamazaki coupled-channel potential. The K−K−pp state has a significantly increased density where the two nucleons are located very close to each other, in spite of the inner NN repulsion. Relativistic corrections on the calculated non-relativistic results indicate substantial lowering of the bound-state masses, especially of K−K−pp, toward the kaon condensation regime. The fact that the recently observed binding energy of K−pp is much larger (by a factor of 2) than the originally predicted one may infer an enhancement of the interaction in dense nuclei by about 25% possibly due to chiral symmetry restoration. In this respect some qualitative accounts are given based on “clearing QCD vacuum” model of Brown, Kubodera and Rho.

Ultracold Fermi gas in a single-mode cavity: Cavity-mediated interaction and BCS-BEC evolution

We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective $s$-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.

Kinetics and energy states of nanoclusters in the initial stage of homogeneous condensation at high supersaturation degrees

The condensation of metal vapor in an inert gas is studied by the molecular dynamics method. Two condensation regimes are investigated: with maintenance of partial pressure of the metal vapor and with a fixed number of metal atoms in the system. The main focus is the study of the cluster energy distribution over the degrees of freedom and mechanisms of the establishment of thermal equilibrium. It is shown that the internal temperature of a cluster considerably exceeds the buffer gas temperature and the thermal balance is established for a time considerably exceeding the nucleation time. It is found that, when the metal vapor concentration exceeds 0.1 of the argon concentration, the growth of clusters with the highest possible internal energy occurs, the condensation rate being determined only by the rate of heat removal from clusters.

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev—Petviashvili I (KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen—Cooper—Schrieffer (BCS) regime, Bose—Einstein condensate (BEC) regime, and unitarity regime. One-lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.

The role of local repulsive interactions on superconductor quantum critical points

The study of superconductivity in multi-band systems is relevant for a variety of materials of actual interest. High Tc cuprates, the new Fe-based materials and heavy fermion superconductors are multi-band systems and this feature must be taken into account for a proper description of their properties. In this paper we study superconductivity in two-band systems. One of the bands is a wide band of conduction electrons. The other is a narrow band of f or d character with an attractive interaction among quasi-particles in neighboring sites and a local repulsive interaction U. These bands are coupled by hybridization, which can be controlled by external pressure allowing to probe the phase diagram of these systems. First, we consider the case of weak repulsive interactions for which a mean-field approximation is satisfactory. We obtain the zero temperature phase diagram for weak and strong attractive interactions. We show that in the presence of U the crossover from the BCS to the Bose–Einstein Condensation (BEC) regime at strong attractive couplings remains smooth. Next we consider the case of strong repulsive U and introduce a Hubbard-I approximation to deal with this interaction. We obtain zero temperature phase diagrams as functions of hybridization and the strength of the repulsive and attractive interactions. We consider the cases of extended s-wave and d-wave symmetry of the order parameter.