arXiv subjects

Rainer Koch

Publications and source records attributed to Rainer Koch.

7 recordsLinked to original sources

arXiv2025

Evidence on the incompatibility of smoothed particle hydrodynamics and eddy viscosity models for large eddy simulations

In this work, we will present evidence for the incompatibility of Smoothed Particle Hydrodynamics (SPH) methods and eddy viscosity models. Taking a coarse-graining perspective, we physically argue that SPH methods operate intrinsically as Lagrangian Large Eddy Simulations (LES) for turbulent flows with strongly overlapping discretization elements. However, these overlapping elements in combination with numerical errors cause a significant amount of implicit subfilter stresses (SFS). Considering a Taylor-Green flow at $Re=10^4$, the SFS will be shown to be relevant where turbulent fluctuations are created, explaining why turbulent flows are challenging even for current SPH methods. Although one might hope to mitigate the implicit SFS using eddy viscosity models, we show a degradation of the turbulent transition process, which is rooted in the non-locality of these methods.

physics.flu-dyn↗

arXiv2022

Smoothed Particle Hydrodynamics Physically Reconsidered -- The Relation to Explicit Large Eddy Simulation and the Issue of Particle Duality

In this work we will identify a novel relation between Smoothed Particle Hydrodynamics (SPH) and explicit Large Eddy Simulation (LES) using a coarse-graining method from Non-Equilibrium Molecular Dynamics (NEMD). While the current literature points at the conclusion that characteristic SPH issues become restrictive for subsonic turbulent flows, we see the potential to mitigate these SPH issues by explicit subfilter stress (SFS) modelling. We verify our theory by various simulations of homogeneous, isotropic turbulence (HIT) at $Re=10^4$ and compare the results to a Direct Numerical Simulation (DNS) reported by Dairay et al. (2017). Although the simulations substantiate our theory, we see another issue arising, which is conceptually rooted in the particle itself, termed as Particle Duality. Finally, we conclude our work by acknowledging SPH as coarse-graining method for turbulent flows, highlighting its capabilities and limitations.

physics.flu-dyn↗

arXiv2021

Fluid Dynamics Beyond the Continuum -- A Physical Perspective on Large Eddy Simulation

In this work, we will present a physically consistent theory to derive the governing equations of the Large Eddy Simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable simulations of turbulent flows. Therefore, we assume that a coarse-grained fluid element, subsequently called super fluid element, can be locally defined comprising a large number of smaller elementary fluid elements. Then, similar to non-equilibrium molecular dynamics (NEMD), in which the transport equations of an elementary fluid element can be consistently reconstructed from the local, collective dynamics of molecules, the transport equations of a super fluid element can be derived from the local, collective dynamics of elementary fluid elements. Interestingly, we find: (a) Favre filtering is a physical consistency condition, (b) why Boussinesq's hypothesis in conjunction with eddy viscosity models is commonly employed in LES and (c) that the LES framework might be more than a numerical turbulence model for computational fluid dynamics (CFD).

physics.flu-dyn↗

arXiv2020

Implicit Molecular Stresses in Weakly-Compressible Particle-Based Discretization Methods for Fluid Flow

Weakly-compressible particle-based discretization methods, utilized for the solution of the subsonic Navier-Stokes equation, are gaining increasing popularity in the fluid dynamics community. One of the most popular among these methods is the weakly-compressible smoothed particle hydrodynamics (WCSPH). Since the dynamics of a single numerical particle is determined by fluid dynamic transport equations, the particle per definition should represent a homogeneous fluid element. However, it can be easily argued that a single particle behaves only pseudo-Lagrangian as it is affected by volume partition errors and can hardly adapt its shape to the actual fluid flow. Therefore, we will assume that the kernel support provides a better representative of an actual fluid element. By means of non-equilibrium molecular dynamics (NEMD) analysis, we derive isothermal transport equations for a kernel-based fluid element. The main discovery of the NEMD analysis is a molecular stress tensor which may serve to explain current problems encountered in applications of weakly-compressible particle-based discretization methods.

physics.flu-dyn↗

arXiv2019

Towards DeepSpray: Using Convolutional Neural Network to post-process Shadowgraphy Images of Liquid Atomization

This technical report investigates the potential of Convolutional Neural Networks to post-process images from primary atomization. Three tasks are investigated. First, the detection and segmentation of liquid droplets in degraded optical conditions. Second, the detection of overlapping ellipses and the prediction of their geometrical characteristics. This task corresponds to extrapolate the hidden contour of an ellipse with reduced visual information. Third, several features of the liquid surface during primary breakup (ligaments, bags, rims) are manually annotated on 15 experimental images. The detector is trained on this minimal database using simple data augmentation and then applied to other images from numerical simulation and from other experiment. In these three tasks, models from the literature based on Convolutional Neural Networks showed very promising results, thus demonstrating the high potential of Deep Learning to post-process liquid atomization. The next step is to embed these models into a unified framework DeepSpray.

cs.CV↗

arXiv2019

Influence of the ambient pressure on the liquid accumulation and on the primary spray in prefilming airblast atomization

The influence of the ambient pressure on the breakup process is investigated by means of PIV and shadowgraphy in the configuration of a planar prefilming airblast atomizer. The ambient pressure is varied from 1 to 8 bar. Other investigated parameters are the gas velocity and the film loading. From single-phase PIV measurements, it is found that the gas velocity in the vicinity of the prefilmer partly matches the analytical profile from the near-wake theory. The characteristics of the liquid accumulation are extracted from the shadowgraphy images of the liquid phase directly downstream of the prefilmer. Two different characteristic lengths, as well as the ligament velocity and a breakup frequency are determined. In addition, the droplets generated directly downstream of the liquid accumulation are captured. Hence, the spray Sauter Mean Diameter (SMD) and the mean droplet velocity are given for each operating point. The novelty of this study is that a scaling law of these quantities with regard to ambient pressure is derived. A correlation is observed between the characteristic length of the accumulation and the SMD, thus reinforcing the idea that the liquid accumulation determines the primary spray characteristics. In this paper, a threshold to distinguish the zones between primary and secondary breakup is proposed based on an objective criterion. It is also shown that taking non-spherical droplets into account significantly modifies the shape of the dropsize distribution, thus stressing the need to use shadowgraphy when investigating primary breakup. Additionally, the ambient pressure and the velocity are varied accordingly to keep the aerodynamic stress $\rho_g U_g^2$ constant. This leads to almost identical liquid accumulation and spray characteristics.

physics.flu-dyn↗

arXiv2018

On the use of circulant matrices for the stability analysis of recent weakly compressible SPH methods

In this study, a linear stability analysis is performed for different Weakly Compressible Smooth Particle Hydrodynamics (WCSPH) methods on a 1D periodic domain describing an incompressible base flow. The perturbation equation can be vectorized and written as an ordinary differential equation where the coefficients are circulant matrices. The diagonalization of the system is equivalent to apply a spatial discrete Fourier transform. This leads to stability conditions expressed by the discrete Fourier transform of the first and second derivatives of the kernel. Although spurious modes are highlighted, no tensile nor pairing instabilities are found in the present study, suggesting that the perturbations of the stresses are always damped if the base flow is incompressible. The perturbations equation is solved in the Laplace domain, allowing to derive an analytical solution of the transient state. Also, it is demonstrated analytically that a positive background pressure combined with the uncorrected gradient operator leads to a reordering of the particle lattice. It is also shown that above a critical value, the background pressure leads to instabilities. Finally, the dispersion curves for inviscid and viscous flows are plotted for different WCSPH methods and compared to the continuum solution. It is observed that a background pressure equal to $\rho c^2$ gives the best fidelity to predict the propagation of a sound wave. When viscosity effects are taken into account, the damping of pressure fluctuations show the best agreement with the continuum for $p_{back} \sim \rho c^2/2$.

physics.comp-ph↗