PT Unknown
AU Ren, H
TI Investigation of the impact of non-ideal fluid states on the classical nucleation theory
PD 01
PY 2024
DI 10.17185/duepublico/82851
LA en
DE Nucleation theory; Real gas; Carbon dioxide; Nucleation model
AB Condensation is a significant topic in engineering areas. For example, during the expansion process within a steam turbine, condensing steam may form droplets which can reduce the machine’s efficiency or even damage the blades. Hence, understanding this phenomenon is a hard requirement to minimise such damage or, in turn, to utilise the phenomenon under certain conditions. Nucleation or droplet formation, normally regarded as the first step of condensation, may determine whether condensation occurs. Thus, numerous studies have been conducted to build the first understanding of nucleation, namely the nucleation theory. Amount this, the so-called classical nucleation theory (CNT) is popular which describes the homogeneous nucleation process and is widely used in engineering calculations. The CNT partly considers the ideal gas law and is normally applied for steam at low pressures exhibiting semi-ideal states. However, it was found later that the CNT might not reflect the nucleation process of real gases correctly, because real gases do not follow the ideal gas law. To predict the nucleation process of real gases, modifications to the classical nucleation model have been made. However, from the author’s knowledge, none of them has been widely proven. The reason could be that the modifications did not include a review of the CNT from the perspective of real gases. This may also prevent an individual discussion on nucleation models because they normally have to be applied in conjunction with a droplet growth model. Hence, the presented work intends to check the validity of CNT from the perspective of real gases and to develop a nucleation model for real gases, by following the classical derivation process from the thermodynamic-kinetical aspect. To achieve this goal, the assumptions made in the CNT regarding the ideal gas law are identified and appropriately modified by considering the real gas equation of state. Firstly, models of the elevation in Gibbs free energy based on various approaches of the equation of state are concretely derived and compared, to analyse the impact of real gases on a simple vapourdroplet system. Secondly, an inconsistency is identified in the classical equilibrium droplet distribution within a supersaturated vapour against one of its significant assumptions as the fluid state exhibits a low compressibility factor. To eliminate this inconsistency, a method is presented by which the equilibrium droplet distribution of a real gas is calculated. It shows plausible results at relatively low reduced temperatures and has limitation at relatively high reduced temperatures due to uncertainty in solving real gas equation of state. Furthermore, the presented work assumes an additional nucleation of small droplets to the CNT, increasing the evaluated nucleation rate in principle. Finally, different nucleation models are applied to calculate the condensation process with constant expansion rates. To focus on the nucleation process, the supercooling at the Wilson point is considered the key parameter. The comparison between calculation results exhibits a quasi-linear correlation between the supercooling at Wilson point and the logarithm of expansion rate. An extension of the “peak” of nucleation rate can be detected at Wilson points very close to the critical point, leading to an evident deviation between the Wilson supercooling and the maximal supercooling. Furthermore, the calculation results are compared with experiments regarding CO2, R12, R22, and water in Laval nozzles. It is found in general that the classical model overpredicts the nucleation rate. In contrast, the presented models with the additional nucleation agree with the test results regarding the supercooling at Wilson points.
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