Theresa Trummler

In this paper, we investigate two-dimensional direct numerical simulations of a transcritical shear layer. Three configurations are chosen, which are distinguished by the level of presence of two-phase phenomena. The thermodynamic model is based on a cubic equation of state. It was extended for multicomponent mixtures, and it is able to account for vapor–liquid equilibrium. The thermodynamic modeling with phase-transition is validated using experimental data from the literature. Special focus is put on the effect of the density gradient and the density changes caused by phase-transition on the development of the turbulent shear layer and the associated mixing. In addition to this, the vorticity distribution and the components of its transport equation are analyzed and compared for the different configurations.

Mixing under high pressure conditions plays a central role in several engineering applications, such as direct-injection engines and liquid rocket engines. Numerical flow simulations have become a complementary tool to study the mixing process under these conditions but require complex thermodynamic modeling as well as validation with accurate experimental data. For this reason, we use experiments of supercritical single-phase jet mixing from the literature, where the mixing is quantified by the mixture speed of sound, as a reference for our work. We here focus on the thermodynamic modeling of multi-component flows under high pressure conditions and the analytical calculation of the mixture speed of sound. Our thermodynamic model is based on cubic equations of state extended for multi-components. Using an extension of OpenFOAM, we perform large-eddy simulations of hexane and pentane injections and compare our results with the experimentally measured mixture speed of sound at specific positions. The simulation results show the same characteristic trends, indicating that the mixing effects are well reproduced in the simulations. Additionally, the effect of the sub-grid scale modeling is assessed by comparing results using different models (Smagorinsky, Vreman, and Wall-Adapting Local Eddy-viscosity). The comprehensive simulation data presented here, in combination with the experimental data, provide a benchmark for numerical simulations of jet mixing in high pressure conditions.

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232, 74–89 (2005)]. With this formulation, all well-known cubic equations of state can be described with a certain pair of values, which allow for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave–Redlich–Kwong and Peng–Robinson and the Redlich–Kwong–Peng–Robinson equation of state. The first two assume a universal critical compressibility factor and are, therefore, only suitable for fluids with a matching critical compressibility. The Redlich–Kwong–Peng–Robinson overcomes this limitation by considering the equation of state parameter as a function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. Additionally, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. We also provide an implementation of the generalized form in OpenFOAM.

We study the segregation of emulsions in decaying turbulence using direct numerical simulations in combination with the volume of fluid method. To this end, we generate emulsions in forced homogeneous isotropic turbulence and then turn the forcing off and activate the gravitational acceleration. This allows us to study the segregation process in decaying turbulence and under gravity. We consider non-iso-density emulsions, where the dispersed phase is the lighter one. The segregation process is driven by both the minimization of the potential energy achieved by the sinking of the heavier phase as well as the minimization of the surface energy achieved by coalescence. To study these two processes and their impacts on the segregation progress in detail, we consider different buoyancy forces and surface tension coefficients in our investigation, resulting in five different configurations. The surface tension coefficient also alters the droplet size distribution of the emulsion. Using the three-dimensional simulation results and the monitored data, we analyze the driving mechanisms and their impact on the segregation progress in detail. We propose a dimensionless number that reflects the energy release dominating the segregation. Moreover, we evaluate the time required for the rise of the lighter phase and study correlations with the varied parameters: gravitational acceleration and surface tension coefficient.

We study turbulent emulsions and the emulsification process in homogeneous isotropic turbulence (HIT) using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). For generating a turbulent flow field, we employ a linear forcing approach augmented by a proportional‐integral‐derivative (PID) controller, which ensures a constant turbulent kinetic energy for two phase flow scenarios and accelerates the emulsification process. For the simulations, the density ratio of dispersed and carrier phases is chosen to be similar to that of oil and water (0.9), representing a typical application. We vary the turbulence intensity and the surface tension coefficient. Thus, we modulate those parameters that directly affect the Hinze scale, which is expected to be the most stable maximum droplet diameter in emulsions in HIT. The considered configurations can be characterized with Taylor Reynolds numbers in the range of 100–140 and Weber numbers, evaluated with the velocity fluctuations and the integral length scale, of 4–70. Using the 3‐D simulation results, we study the emulsification process as well as the emulsions at a statistically stationary state. For the latter, droplet size distributions are evaluated and compared. We observe a Hinze scale similarity of the size distributions considering a fixed integral length scale, that is, similar Hinze scales obtained at different turbulence intensities or for different fluid properties result in similar distributions.

A direct numerical simulation database of bubbly channel flows at friction Reynolds number 180 and with three different global void fractions has been used to perform a multiscale analysis of the anisotropy of the Reynolds stress tensor, the dissipation tensor, and the subgrid-scale (SGS) tensor in order to characterize the turbulence for a wide range of scales down to the smallest structures occurring in the flow. Based on the hypothesis of Kolmogorov, the non-linear turbulent energy transfer is expected to result in a loss of directional information such that, for a sufficiently high Reynolds number, the small-scale turbulence is expected to be isotropic and universal. The present analysis reveals that the presence of the bubbles increases the anisotropy of the flow which persists down to the smallest scales of motion, even for the dissipation and SGS tensor. This has implications for the complete landscape of turbulence modeling approaches ranging from large eddy simulation, over hybrid approaches to Reynolds averaged Navier–Stokes based modeling.

The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.

We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure, and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the cavitating liquid is a barotropic thermodynamic equilibrium model. Compressibility of all phases is considered in order to capture the shock wave of the bubble collapse. After validating the model with an analytical energy partitioning model, simulations of collapsing wall-attached bubbles with different stand-off distances are performed. The effect of the non-condensable gas on rebound and damping of the emitted shock wave is well captured.