Traveling gravity water waves with critical layers

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period. An important part of the analysis is a fairly complete description of the local geometry of the so-called kernel equation, and of the small-amplitude solutions. Finally, we investigate the asymptotic behavior of the bifurcating solutions.Comment: 31 page

A Study of Rotational Water Waves using Bifurcation Theory

This thesis is concerned with the water wave problem. Using local bifurcation we establish small-amplitude steady and periodic solutions of the Euler equations with vorticity. Our approach is based on that of Ehrnström, Escher and Wahlén \cite{EEW11}, the main difference being that we use new bifurcation parameters. The bifurcation is done both from a one-dimensional and a two-dimensional kernel, the latter bifurcation giving rise to waves having more than one crest in each minimal period. We also give a novel and rudimentary proof of a key lemma establishing the Fredholm property of the elliptic operator associated with the water wave problem. Furthermore, we investigate derivatives of the bifurcation curve, and present a new result for the corresponding linear problem

Curvature Corrections Remove the Inconsistencies of Binary Classical Nucleation Theory

The study of nucleation in fluid mixtures exposes challenges beyond those of pure systems. A striking example is homogeneous condensation in highly surface-active water-alcohol mixtures, where classical nucleation theory yields an unphysical, negative number of water molecules in the critical embryo. This flaw has rendered multicomponent nucleation theory useless for many industrial and scientific applications. Here, we show that this inconsistency is removed by properly incorporating the curvature dependence of the surface tension of the mixture into classical nucleation theory for multicomponent systems. The Gibbs adsorption equation is used to explain the origin of the inconsistency by linking the molecules adsorbed at the interface to the curvature corrections of the surface tension. The Tolman length and rigidity constant are determined for several water-alcohol mixtures and used to show that the corrected theory is free of physical inconsistencies and provides accurate predictions of the nucleation rates. In particular, for the ethanol-water and propanol-water mixtures, the average error in the predicted nucleation rates is reduced from 11–15 orders of magnitude to below 1.5. The curvature-corrected nucleation theory opens the door to reliable predictions of nucleation rates in multicomponent systems, which are crucial for applications ranging from atmospheric science to research on volcanos. © 2020 American Physical SocietyacceptedVersion© 2020. This is the authors' accepted and refereed manuscript to the chapter

Extrapolating into no man's land enables accurate estimation of surface properties with multiparameter equations of state

Thermodynamic properties of homogeneous fluids in the metastable and unstable regions are needed to describe confined fluids, interfaces, nucleating embryos and estimate critical mass flow rates. The most accurate equations of state (EoS) called multiparameter EoS, have a second, non-physical Maxwell loop that renders predictions unreliable in these regions. We elaborate how information from the stable region can be used to reconstruct the metastable and unstable regions. For a simple interaction potential, comparison to results from molecular simulations reveals that isochoric expansion of the pressure from stable states reproduces simulation results in the metastable regions. By constructing a dome that extends above the critical point, we obtain an extrapolated pressure from multiparameter EoS that is free of second Maxwell loops. A reconstructed EoS is developed next, by integrating the extrapolated pressure from a stable state to obtain the Helmholtz energy. The consistency of the reconstructed EoS is gauged by computing phase equilibrium densities, pressures, and enthalpies of evaporation, which are in reasonable agreement with experimental values. Combined with density gradient theory, the reconstructed EoS yields surface tensions of water, carbon dioxide, ammonia, hydrogen and propane that deviate, on average, 4.4%, 1.6%, 6.0%, 0.7% and 5.4% from experimental values respectively. The results reveal a potential to develop more accurate extrapolation protocols, which can be leveraged to obtain prediction of metastable properties, surface properties or used as constraints in fitting multiparmeter EoS.Extrapolating into no man's land enables accurate estimation of surface properties with multiparameter equations of statepublishedVersio

Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

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Heat-driven snow production applying ejector and natural refrigerant

An effect of climate change is fewer cold days and less natural snow at lower elevations. This has spurred the interest in temperature independent snow (TIS) production, i.e., refrigeration technologies that can produce snow at ambient temperatures above zero. Commercially available TIS systems require a higher power consumption than conventional systems, i.e., snow lances and guns. Thus, to ensure that future snow-making sites are sustainable, it is necessary to develop solutions with a minimal environmental footprint. One possibility is to utilize surplus heat from industrial processes or from a district heating network to drive snow-making systems. Examples of heat driven refrigeration technologies fit for this purpose are absorption cooling and ejector cooling, both applying natural refrigerants. This paper evaluates a solution for heat driven ejector-based snow making systems: a vacuum ice slurry system using water (R718) as refrigerant. The required amount of driving heat and its required minimum temperature level largely depend on the ejector characteristics. Thus, to enable a proper evaluation, detailed numerical simulations of the ejector design and its efficiency were performed, at different temperature levels of driving heat and ambient temperatures. Results were used as input to estimate the overall performance, in terms of specific energy consumption (per m3 produced snow), compared to other TIS systems. The ejector-based system can be driven by low-grade heat (80 °C) and is shown to be highly efficient if cold cooling water (≤ 10°C) is available.Heat-driven snow production applying ejector and natural refrigerantacceptedVersio

Estimating metastable thermodynamic properties by isochoric extrapolation from stable states

The description of metastable fluids, those in local but not global equilibrium, remains an important problem of thermodynamics, and it is crucial for many industrial applications and all first order phase transitions. One way to estimate their properties is by extrapolation from nearby stable states. This is often done isothermally, in terms of a virial expansion for gases or a Taylor expansion in density for liquids. This work presents evidence that an isochoric expansion of pressure at a given temperature is superior to an isothermal density expansion. Two different isochoric extrapolation strategies are evaluated, one best suited for vapors and one for liquids. Both are exact for important model systems, including the van der Waals equation of state. Moreover, we present a simple method to evaluate all the coefficients of the isochoric expansion directly from a simulation in the canonical ensemble. Using only the properties of stable states, the isochoric extrapolation methods reproduce simulation results with Lennard-Jones potentials, mostly within their uncertainties. The isochoric extrapolation methods are able to predict deeply metastable pressures accurately even from temperatures well above the critical. Isochoric extrapolation also predicts a mechanical stability limit, i.e., the thermodynamic spinodal. For water, the liquid spinodal pressure is predicted to be monotonically decreasing with decreasing temperature, in contrast to the re-entrant behavior predicted by the direct extension of the reference equation of state. © 2024 Author(s).Estimating metastable thermodynamic properties by isochoric extrapolation from stable statesacceptedVersio

Choice of reference, influence of non-additivity and present challenges in thermodynamic perturbation theory for mixtures

This work revisits the fundamentals of thermodynamic perturbation theory for fluid mixtures. The choice of reference and governing assumptions can profoundly influence the accuracy of the perturbation theory. The statistical associating fluid theory for variable range interactions of the generic Mie form equation of state is used as a basis to evaluate three choices of hard-sphere reference fluids: single component, additive mixture, and non-additive mixture. Binary mixtures of Lennard-Jones fluids are investigated, where the ratios of σ (the distance where the potential is zero) and the ratios of ϵ (the well depth) are varied. By comparing with Monte Carlo simulations and results from the literature, we gauge the accuracy of different theories. A perturbation theory with a single-component reference gives inaccurate predictions when the σ-ratio differs significantly from unity but is otherwise applicable. Non-additivity becomes relevant in phase-equilibrium calculations for fluids with high ϵ-ratios or when the mixing rule of σ incorporates non-additivity through an adjustable parameter. This can be handled in three ways: by using a non-additive hard-sphere reference, by incorporating an extra term in the additive hard-sphere reference, or with a single-component reference when the σ-ratio is close to unity. For σ- and ϵ-ratios that differ significantly from unity, the perturbation theories overpredict the phase-equilibrium pressures regardless of reference. This is particularly pronounced in the vicinity of the critical region for mixtures with high ϵ-ratios. By comparing with Monte Carlo simulations where we compute the terms in the perturbation theory directly, we find that the shortcomings of the perturbation theory stem from an inaccurate representation of the second- and third-order perturbation terms, a2 and a3. As mixtures with molecules that differ significantly in size and depths of their interaction potentials are often encountered in industrial and natural applications, further development of the perturbation theory based on these results is an important future work.acceptedVersionThis is the authors’ accepted and refereed manuscript to the article. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in (citation of published article) and may be found at http://dx.doi.org/10.1063/1.514277

Free energy of critical droplets—from the binodal to the spinodal

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo in the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT), this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at 2.5σ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results for critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to the second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible regions. However, it is imprecise for the smallest droplets and largest metastabilities since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of the formation of critical droplets for the entire metastability range and all temperatures examined and deviates from density gradient theory by less than one kB

Local area cooling versus broad area cooling for boil-off reduction in large-scale liquid hydrogen storage tanks

Future use of liquid hydrogen (Image 1 ) as an effective energy carrier will require elimination or minimization of hydrogen boil-off that is not utilized by demands in the value chain. The present work promotes local area cooling (LAC) as a promising boil-off reduction technology. In contrast to the more conventional broad area cooling (BAC), LAC targets local, concentrated heat flows e.g. through tank support structures. This yields important practical benefits, especially for large-scale tanks, due to the order-of-magnitude reduction in the size of the cooling system. Such benefits include lower capital costs and simpler installation, maintenance and coolant management. LAC applied outside the outer tank wall is particularly attractive for tanks with evacuated insulation. In a series of numerical studies, we use the finite element method to evaluate the thermal performance of LAC and BAC in the context of ship-borne Image 1 transport. The studies concern 40 000 m3-capacity, skirt-supported tanks insulated using evacuated perlite or helium-filled polyurethane (HePUR) foam. For the perlite-insulated tank, LAC and BAC with liquid nitrogen coolant can reduce the daily boil-off rate from 0.04%/day to, respectively, 0.011%/day and 0.004%/day. The corresponding numbers for CO2-based refrigeration are 0.031%/day and 0.028%/day. For the HePUR-insulated tank, which has a higher baseline boil-off rate of 0.24%/day, reduced boil-off rates down to 0.17%/day and 0.04%/day are achievable using LAC and BAC, respectively. LAC and BAC both offer increased power efficiency in comparison to reliquefaction only.Local area cooling versus broad area cooling for boil-off reduction in large-scale liquid hydrogen storage tankspublishedVersio