Browsing by Author "Stierle, Rolf"

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Open Access
Characterisation of the transient mixing behaviour of evaporating near-critical droplets
(2023) Steinhausen, Christoph; Gerber, Valerie; Stierle, Rolf; Preusche, Andreas; Dreizler, Andreas; Gross, Joachim; Weigand, Bernhard; Lamanna, Grazia
With technical progress, combustion pressures have been increased over the years, frequently exceeding the critical pressure of the injected fluids. For conditions beyond the critical point of the injected fluids, the fundamental physics of mixing and evaporation processes is not yet fully understood. In particular, quantitative data for validation of numerical simulations and analytical models remain sparse. In previous works, transient speed of sound studies applying laser-induced thermal acoustics (LITA) have been conducted to investigate the mixing behaviour in the wake of an evaporating droplet injected into a supercritical atmosphere. LITA is a seedless, non-intrusive measurement technique capable of direct speed of sound measurements within these mixing processes. The used setup employs a high-repetition-rate excitation laser source and, therefore, allows the acquisition of time-resolved speed of sound data. For the visualisation of the evaporation process, measurements are accompanied by direct, high-speed shadowgraphy. In the present work, the measured speed of sound data are evaluated by applying an advection-controlled mixing assumption to estimate both the local mole fraction and mixing temperature. For this purpose, planar spontaneous Raman scattering results measured under the same operating conditions are evaluated using an advection-controlled mixing assumption with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Successively, the resulting concentration–temperature field is used for the estimation of local mixture parameters from the detected speed of sound data. Moreover, models using the PC-SAFT equation of state and the NIST database for the computation of the speed of sound are compared. The investigations indicate a classical two-phase evaporation process with evaporative cooling of the droplet. The subsequent mixing of fluid vapour and ambient gas also remains subcritical in the direct vicinity of the droplet.
Open Access
Development of hydrodynamic density functional theory for mixtures and application to droplet coalescence
(Stuttgart : Universität Stuttgart, Institut für Technische Thermodynamik und Thermische Verfahrenstechnik, 2021) Stierle, Rolf; Groß, Joachim (Prof. Dr.-Ing.)
Predicting accurately coalescence phenomena is critical to the accurate description of the hydrodynamics of fluids and their mixtures. A promising framework for the development of models for such phenomena is dynamic density functional theory. Dynamic density functional theory enables the analysis of dynamical processes in inhomogeneous systems of pure fluids and fluid mixtures at the molecular level. In this work, a hydrodynamic density functional theory model for mixtures in conjunction with Helmholtz energy functionals based on the PC-SAFT equation of state is proposed, that obeys the first and second law of thermodynamics and simplifies to the isothermal Navier-Stokes equation for homogeneous systems. The hydrodynamic density functional theory model is derived from a variational principle and accounts for both viscous forces and diffusive molecular transport. A Maxwell-Stefan model is applied for molecular transport. This work identifies a suitable expression for the driving force for molecular diffusion of inhomogeneous systems that captures the effect of interfacial tension. The proposed hydrodynamic density functional theory is a non-local theory that requires the computation of weighted (spatial averaged) densities around each considered spatial coordinate by convolution, which is computationally expensive. This work uses Fourier-type transforms to determine the weighted densities. A pedagogical derivation is presented for the efficient computation of the convolution integrals occurring in the Helmholtz energy functionals in Cartesian, cylindrical, and spherical coordinates on equidistant grids using fast Fourier and similar transforms. The applied off-the-shelf algorithms allow to reduce dimensionality and complexity of many practical problems. Furthermore, an algorithm for a fast first-order Hankel transform is proposed, allowing fast and easy density functional theory calculations in rotationally symmetric systems. Application of the hydrodynamic density functional theory model using a well-balanced finite-volume scheme to one-dimensional droplet and bubble coalescence of pure fluids and binary mixtures is presented. The required transport coefficients, shear viscosity and Maxwell-Stefan diffusion coefficients, are obtained by applying entropy scaling to inhomogeneous fluids. The considered systems show a qualitative difference in the coalescence characteristics of droplets compared to bubbles. This constitutes a first step towards predicting the phase rupture leading to coalescence using dynamic density functional theory.