## Large eddy simulations of reacting and non-reacting transcritical fuel sprays using multiphase thermodynamics

Fathi, M., Hickel, S., Roekaerts, D. (2022)*Physics of Fluids* 34: 085131. doi: 10.1063/5.0099154

We present a novel framework for high-fidelity simulations of inert and reacting sprays with highly accurate and computationally efficient models for complex real-gas effects in high-pressure environments, especially for the hybrid subcritical/supercritical mode of evaporation during the mixing of fuel and oxidizer at transcritical conditions.

## Rapid multi-component phase-split calculations using volume functions and reduction methods

Fathi, M., Hickel, S. (2021) *AIChE Journal *67: e17174. doi: 10.1002/aic.17174

We present a new family of fast and robust methods for the calculation of the vapor–liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy.

## Multi-component vapor-liquid equilibrium model for LES of high-pressure fuel injection and application to ECN Spray A

Matheis, J., Hickel, S. (2018) *International Journal of Multiphase Flow *99: 294-311. doi: 10.1016/j.ijmultiphaseflow.2017.11.001

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component subcritical two-phase states via a homogeneous mixture approach.

## Large-eddy simulation of turbulent, cavitating flow inside a 9-hole Diesel injector including needle movement

Örley, F., Hickel, S., Schmidt, S.J., Adams, N.A. (2017)*International Journal of Engine Research* 18:195-211. doi: 10.1177/1468087416643901

We investigate the turbulent multiphase flow inside a nine-hole common rail Diesel injector during a full injection cycle of ISO 4113 diesel fuel into air by implicit large-eddy simulation (LES). The simulation includes a prescribed needle movement obtained from a one-dimensional multi-domain simulation.

## Multi-component vapor-liquid equilibrium model for LES and application to ECN Spray A

Matheis, J., Hickel, S. (2016)

Proceedings of the 2016 Summer Program, Center for Turbulence Research, Stanford University. (also available online on arXiv:1609.08533)

We present and evaluate a detailed multi-species two-phase thermodynamic equilibrium model for large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model can represent the coexistence of supercritical states and multi-component subcritical two-phase states.

## Efficient implicit LES method for the simulation of turbulent cavitating flows

Egerer, C.P., Schmidt, S.J., Hickel, S., Adams, N.A. (2016) *Journal of Computational Physics* 316: 453-469. doi: 10.1017/10.1016/j.jcp.2016.04.021

We present a numerical method for efficient large-eddy simulation of compressible liquid flows with cavitation based on an implicit subgrid-scale model. Phase change and subgrid-scale interface structures are modeled by a homogeneous mixture model that assumes local thermodynamic equilibrium. Unlike previous approaches, emphasis is placed on operating on a small stencil (at most four cells).

## Large-eddy simulation of coaxial LN2/GH2 injection at trans- and supercritical conditions

Müller, H., Pfitzner, M., Matheis, J., Hickel, S. (2015) *Journal of Propulsion and Power *32: 46-56. doi: 10.2514/1.B35827

Large-eddy simulations are carried out for the coaxial injection of liquid nitrogen and preheated hydrogen at supercritical pressures. A novel volume-translation method on the basis of the cubic Peng–Robinson equation of state is introduced for the use in multispecies large-eddy simulations and is tested for both trans- and supercritical injection conditions.

## Large-eddy simulation of cavitating nozzle flow and primary jet break-up

Örley, F., Trummler, T., Hickel, S., Mihatsch, M.S., Schmidt, S.J., Adams, N.A. (2015)*Physics of Fluids* 27: 086101. doi: 10.1063/1.4928701

We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics.

## Cut-element based immersed boundary method for moving geometries in compressible liquid flows with cavitation

Örley, F., Pasquariello, V., Hickel, S., Adams, N.A. (2015) *Journal of Computational Physics* 283: 1-22. doi: 10.1016/j.jcp.2014.11.028

The conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on Cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries. We demonstrate that an approximation of moving interfaces by a level-set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water. By introducing an exact reconstruction of the cut-cell properties directly based on a surface triangulation of the immersed boundary, we are able to recover the correct flow evolution free of numerical artifacts.

## LES of Temporally Evolving Turbulent Cavitating Shear Layers

Egerer, C., Hickel, S., Schmidt, S., Adams, N.A. (2014)*High Performance Computing in Science and Engineering* ’14: 367-378 doi: 10.1007/978-3-319-10810-0_25

We present LES results of temporally evolving cavitating shear layers. Cavitation is modeled by a homogeneous equilibrium mixture model whereas the effect of subgrid-scale turbulence is accounted for by the Adaptive Local Deconvolution Method (ALDM). We quantitatively compare LES results with experimental data available in the literature.

## Large-eddy simulation of turbulent cavitating flow in a micro channel

Egerer, C.P., Hickel, S., Schmidt, S.J., Adams, N.A. (2014)*Physics of Fluids* 26, 085102. doi: 10.1063/1.4891325

Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture.

## Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics

Lauer, E., Hu, X.Y., Hickel, S., Adams, N.A. (2012) *Computers and Fluids* 69: 1-19. doi: 10.1016/j.compfluid.2012.07.020

In this paper, we investigate the high-speed dynamics of symmetric and asymmetric cavitation bubble-collapse. For this purpose, a sharp-interface numerical model is employed, that includes a numerically efficient evaporation/condensation model.

## Numerical investigation of collapsing cavity arrays

Lauer, E., Hu, X.Y., Hickel, S., Adams, N.A. (2012) *Physics of Fluids *24: 052104. doi: 10.1063/1.4719142

## Implicit Large Eddy Simulation of cavitation in micro channel flows

Hickel, S., Mihatsch, M., Schmidt S.J. (2011)

In *proceedings of the WIMRC 3rd International Cavitation Forum* ; Warwick, UK.; ISBN 978-0-9570404-1-0. arXiv: 1401.6548

We present a numerical method for Large Eddy Simulations (LES) of compressible two-phase flows. The method is validated for the flow in a micro channel with a step-like restriction. This setup is representative for typical cavitating multi-phase flows in fuel injectors and follows an experimental study of Iben *et al. *(2010).