Browsing by Author "Hellmuth, Olaf"
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- ItemAnalytical determination of the nucleation-prone, low-density fraction of subcooled water(Basel : MDPI AG, 2020) Hellmuth, Olaf; Feistel, RainerSubcooled water is the primordial matrix for ice embryo formation by homogeneous and heterogeneous nucleation. The knowledge of the specific Gibbs free energy and other thermodynamic quantities of subcooled water is one of the basic prerequisites of the theoretical analysis of ice crystallization in terms of classical nucleation theory. The most advanced equation of state of subcooled water is the IAPWS G12-15 formulation. The determination of the thermodynamic quantities of subcooled water on the basis of this equation of state requires the iterative determination of the fraction of low-density water in the two-state mixture of low-density and high-density subcooled water from a transcendental equation. For applications such as microscopic nucleation simulation models requiring highly frequent calls of the IAPWS G12-15 calculus, a new two-step predictor-corrector method for the approximative determination of the low-density water fraction has been developed. The new solution method allows a sufficiently accurate determination of the specific Gibbs energy and of all other thermodynamic quantities of subcooled water at given pressure and temperature, such as specific volume and mass density, specific entropy, isothermal compressibility, thermal expansion coefficient, specific isobaric and isochoric heat capacities, and speed of sound. The misfit of this new approximate analytical solution against the exact numerical solution was demonstrated to be smaller than or equal to the misprediction of the original IAPWS G12-15 formulation with respect to experimental values. © 2020 by the authors.
- ItemIce-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension. Part I: Theoretical Foundation(Basel : MDPI, 2020) Hellmuth, Olaf; Schmelzer, Jürn W.P.; Feistel, RainerA recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice-water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10-based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice-water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice-water system was found to amount TK=116K , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to pK=−212MPa , suggesting favor of homogeneous freezing on exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.
- ItemMultivariate non-parametric Euclidean distance model for hourly disaggregation of daily climate data(Wien [u.a.] : Springer, 2021) Görner, Christina; Franke, Johannes; Kronenberg, Rico; Hellmuth, Olaf; Bernhofer, ChristianThe algorithm for and results of a newly developed multivariate non-parametric model, the Euclidean distance model (EDM), for the hourly disaggregation of daily climate data are presented here. The EDM is a resampling method based on the assumption that the day to be disaggregated has already occurred once in the past. The Euclidean distance (ED) serves as a measure of similarity to select the most similar day from historical records. EDM is designed to disaggregate daily means/sums of several climate elements at once, here temperature (T), precipitation (P), sunshine duration (SD), relative humidity (rH), and wind speed (WS), while conserving physical consistency over all disaggregated elements. Since weather conditions and hence the diurnal cycles of climate elements depend on the weather pattern, a selection approach including objective weather patterns (OWP) was developed. The OWP serve as an additional criterion to filter the most similar day. For a case study, EDM was applied to the daily climate data of the stations Dresden and Fichtelberg (Saxony, Germany). The EDM results agree well with the observed data, maintaining their statistics. Hourly results fit better for climate elements with homogenous diurnal cycles, e.g., T with very high correlations of up to 0.99. In contrast, the hourly results of the SD and the WS provide correlations up to 0.79. EDM tends to overestimate heavy precipitation rates, e.g., by up to 15% for Dresden and 26% for Fichtelberg, potentially due to, e.g., the smaller data pool for such events, and the equal-weighted impact of P in the ED calculation. The OWPs lead to somewhat improved results for all climate elements in terms of similar climate conditions of the basic stations. Finally, the performance of EDM is compared with the disaggregation tool MELODIST (Förster et al. 2015). Both tools deliver comparable and well corresponding results. All analyses of the generated hourly data show that EDM is a very robust and flexible model that can be applied to any climate station. Since EDM can disaggregate daily data of climate projections, future research should address whether the model is capable to respect and (re)produce future climate trends. Further, possible improvements by including the flow direction and future OWPs should be investigated, also with regard to reduce the overestimation of heavy rainfall rates.