Marcel Pfeiffer

Universität Stuttgart · Institute of Space Systems

The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple vibrational degrees of freedom. For this, the models of Mathiaud, Mieussens, Pfeiffer, and Brull are combined. In ord...

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built clo...

The BGK model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale flows, in which the Knudsen number varies by several orders of magnitude, is never straightforward. Discrete velocity methods as well as pa...

Utilizing differential atmospheric forces in the Very Low Earth Orbits (VLEO) regime for the control of the relative motion within a satellite formation is a promising option as any thrusting device has tremendous effects on the mission capacity due to the limited weight and size restrictions of small satellites. One possible approach to increase t...

The use of Euler–Lagrange methods on unstructured grids extends their application area to more versatile setups. However, the lack of a regular topology limits the scalability of distributed parallel methods, especially for routines that perform a physical search in space. One of the most prominent slowdowns is the search for halo elements in physi...

A collision-averaged parameter set for air, carbon and the corresponding ionized species for the variable soft sphere collision model is suggested which is suitable for the earth's atmosphere or mars atmosphere, for example. The parameter set is generated through collision integral fits and a number of optimisation steps, so that individual subsets...

The numerical simulation of multi-scale problems and non-equilibrium gas flows is of highest interest as experimental investigations are extremely complicated or impossible. Using the well-established Direct Simulation Monte Carlo (DSMC) method, a highly accurate solution of these flows can be achieved. However, simulations are accompanied by exces...

To achieve a feasible lifetime of several years, most satellites are deployed in orbits higher than 400 km. Drag of residual atmosphere causes a slow orbit decay, resulting in the deorbit of the spacecraft. However, e.g. optical instruments or communication devices would significantly benefit from lower altitudes in the range of 150-250 km. A solut...

The utilisation of the Very Low Earth Orbit (VLEO) region offers significant application specific, technological, operational, and cost benefits. However, attaining sustained and economically viable VLEO flight is challenging, primarily due to the significant, barely predictable and dynamically changing drag caused by the residual atmosphere, which...

Despite the development of an extensive toolbox of multiscale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatiotemporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK e...

We propose a new ES-BGK model for diatomic gases which allows for translational-rotational and translational-vibrational energy exchanges, as given by Landau-Teller and Jeans relaxation equations. This model is consistent with the general definition of the vibrational and rotational collision numbers that are also commonly used in DSMC solvers. It...

The operation of satellites in very low altitudes has significant technical and cost benefits. However, the main problem is the non-negligible aerodynamic drag force which leads to a rapid deterioration of satellite orbits if no adequate means of compensation is available. Passively, the lifetime of the spacecraft can be increased by a reduction in...

The use of Euler-Lagrange methods on unstructured grids extends their application area to more versatile setups. However, the lack of a regular topology limits the scalability of distributed parallel methods, especially for routines that perform a physical search in space. One of the most prominent slowdowns is the search for halo elements in physi...

The utilisation of the Very Low Earth Orbit (VLEO) region offers significant application specific, technological, operational, and cost benefits. However, attaining sustained and economically viable VLEO flight is challenging, primarily due to the significant, barely predictable and dynamically changing drag caused by the residual atmosphere, which...

We propose a new ES-BGK model for diatomic gases which allows for translational-rotational and translational-vibrational energy exchanges, as given by Landau-Teller and Jeans relaxation equations. This model is consistent with the general definition of the vibrational and rotational collision numbers that are also commonly used in DSMC solvers. It...

Despite the development of an extensive toolbox of multi-scale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatio-temporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK...

Radiation modeling is implemented in the highly parallel gas kinetic, open-source plasma simulation suite PICLas. A photon Monte Carlo approach for three-dimensional radiative energy transfer is developed. Since these kind of solvers have the disadvantage of high computational costs and statistical fluctuations, these points are addressed by specif...

Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft. To extend the lifetime of such missions, an efficient propulsion system is required. One solution is Atmosphere-Breathing Electric Propulsion (ABEP) that collects atmospheric particles to be used as propellant for an...

Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft. To extend the lifetime of such missions, an efficient propulsion system is required. One solution is Atmosphere-Breathing Electric Propulsion (ABEP) that collects atmospheric particles to be used as propellant for an...

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighbouring phases, yet their closure far from the continuum needs to be modelled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built c...

Multi-species modeling is implemented for the particle-based ellipsoidal statistical Bhatnagar–Gross–Krook method for monatomic species in the open-source plasma simulation suite PICLas. After a literature review on available multi-species extensions of the kinetic model equations and approaches for the determination of the transport coefficients,...

Euler-Lagrange methods are a common approach for simulation of dispersed particle-laden flow, e.g. in turbomachinery. In this approach, the fluid is treated as continuous phase with an Eulerian field solver whereas the Lagrangian movement of the dispersed phase is described through the equations of motion for each individual particle. In high-perfo...

Multi-species modeling is implemented for the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) for monatomic species in the open-source plasma simulation suite PICLas. After a literature review on available multi-species extensions of the kinetic model equations and approaches for the determination of the transport coefficients,...

This paper demonstrates the efficiency of a modified particle based Ellipsoidal Statistical Bhatnagar-Gross-Krook (ES-BGK) solver to simulate micro-nozzles. For this, the common particle ESBGK algorithm is adapted to handle variable particle weights including the creation of additional particles in regions with low statistical samples and merging o...

Estimating the heat loads on re-entry vehicles is a crucial part of preparing for atmospheric re-entry manoeuvres. Re-entry flows at high altitudes are in the rarefied regime and are governed by high enthalpies and thermodynamic non-equilibrium. Additionally, catalytic gas-surface reactions change the gas flow composition and can have a major influ...

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. Molecular interactions are...

The evaporation behaviour of droplets changes with their size. Most numerical tools to simulate evaporation phenomena of droplets solve macroscopic models such as the Navier-Stokes equations. These numerical tools have an advantage in computational effort compared to tools solving microscopic models such as the Boltzmann equation. However, macrosco...

Atmospheric entries at high velocities can introduce considerable radiative heat fluxes. The calculation of these fluxes can be substantially impacted by different non-equilibrium effects, which are occurring in the surrounding flow. In this paper, the coupled Particle-in-Cell and Direct Simulation Monte Carlo Code PICLas is introduced and the theo...

Over the past half century, a variety of computational fluid dynamics (CFD) methods and the direct simulation Monte Carlo (DSMC) method have been widely and successfully applied to the simulation of gas flows for the continuum and rarefied regime, respectively. However, they both encounter difficulties when dealing with multiscale gas flows in mode...

The Institute of Space Systems (IRS) at the University of Stuttgart, which has successfully flown the small satellite Flying Laptop, and the Small Satellite Student Society (KSat e.V.) are developing a 3U+ CubeSat for innovative technology demonstration, atmospheric research and investigation of satellite demise. The Stuttgart Operated University R...

Modeling of nozzle flow expansions is especially of interest for the development of thrusters for in-space propulsion. Due to the expansion into near-vacuum, the density drops drastically compared to the nozzle throat. However, the simulation of a wide Knudsen number range with a single approach is very challenging. While the Direct Simulation Mont...

The numerical simulation of ion thruster optics is one of the most common applications of particle-based methods in the field of electric propulsion. Over the years, powerful tools for simulation of ion trajectories and charge exchange erosion have been developed and validated. However, not fully conservative physical models have to be applied with...

The simulation of gas and plasma flows in the rarefied up to the continuum regime are of great interest to a multitude of applications ranging from atmospheric entry to electric propulsion. Large density gradients prohibit the use of a single method such as the well-established Direct Simulation Monte Carlo (DSMC) method due to excessive computatio...

This paper investigates three different particle-based continuum methods, the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) and Fokker-Planck (ESFP) methods and the Low Diffusion (LD) method, for a coupling with the direct simulation Monte Carlo (DSMC) method. After a short description of the methods and their implementation, including the...

A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direc...

Motivated by improving the performance of particle-based Monte-Carlo simulations in the transitional regime, Fokker–Planck kinetic models have been devised and studied as approximations of the Boltzmann collision operator. By generalizing the linear drift model, the cubic Fokker–Planck (cubic-FP) and ellipsoidal Fokker–Planck (ES-FP) have been prop...

The simulation of laser-plasma interaction via three- dimensional Particle-In-Cell methods based on higher-order schemes is considered. High-order methods allow for drastically reducing the required number of degrees of freedom while still capturing the complex physical nature of non-linear processes. The suitability of high-order methods for the a...

A high-order hybridizable discontinuous Galerkin spectral element method (HDGSEM) for Particle-In-Cell (PIC) schemes is presented for the simulation of electrostatic applications on three-dimensional unstructured curved meshes. The electrostatic Poisson equation is solved and optionally a Boltzmann relation for the electron species can be used whic...

We present a load balancing strategy for hybrid particle-mesh methods that is based on domain decomposition and element-local time measurement. This new strategy is compared to our previous approach, which assumes a constant weighting factor for each particle to determine the computational load. The timer-based load balancing is applied to a plasma...

In the context of the validation of PICLas, a kinetic particle suite for the simulation of rarefied, non-equilibrium plasma flows, the biased hypersonic nitrogen flow around a blunted cone was simulated with the Direct Simulation Monte Carlo method. The setup is characterized by a complex flow with strong local gradients and thermal non-equilibrium...

The particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model is extended to diatomic molecules and compared with the Direct Simulation Monte Carlo (DSMC) method. For this, an efficient method is developed that optionally allows the handling of quantized vibrational energies. The proposed method is verified with a gas in an adiabat...

The Bhatnagar-Gross-Krook (BGK) model and its extensions (ellipsoidal statistical BGK, Shakhov BGK, and unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this end, different methods are investigated that allow efficient sampling of the Shakhov and the unified target distribu...

The particle-based ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model is extended to diatomic molecules and compared with the Direct Simulation Monte Carlo (DSMC) method. For this an efficient method is developed that optionally allows the handling of quantized vibrational energies. The proposed method is verified with a gas in an adiabati...

In this paper, results of the simulation tools URANUS and PICLas are compared to Plasma wind tunnel experiments. This is done for validation purposes of catalytic modelling within these tools. Therefore, the used experimental setup, from which the discussed simulation case is derived, and challenges in the flow characterization are shown. The main...

The Bhatnagar-Gross-Krook (BGK) model as well as its extensions (ellipsoidal statistical BGK, Shakhov BGK, unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo Method (DSMC). To this end, a method based on the Metropolis-Hastings algorithm is presented that allows efficient sampling of the Shakh...

The numerical simulation of ion thruster optics is one of the most common applications of particle-based methods in the field of electric propulsion. Over the years, powerful tools for simulation of ion trajectories and charge exchange erosion have been developed and validated. The validity of prediction results is high as long as the ion optics sy...

Concepts of a particle-based continuum method have existed for many years. The ultimate goal is to couple such a method with the Direct Simulation Monte Carlo (DSMC) in order to bridge the gap of numerical tools in the treatment of the transitional flow regime between near-equilibrium and rarefied gas flows. For this purpose, the Low Diffusion (LD)...

For the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan, the chemistry modeling of polyatomic molecules is implemented in the direct simulation Monte Carlo method within the reactive plasma flow solver PICLas. An additional reaction condition as well as the consideration of the vibrational degrees of freedom is described in the...

The expansion of a plasma plume resulting from laser ablation plays an important role in a large number of applications, e.g., material processing, medical laser applications or novel space propulsion concepts. Here, a high-order three-dimensional Particle-In-Cell code is used to simulate such a plasma plume expansion. A major challenge in this kin...

In order to enable the numerical simulation of rarefied plasma flows in thermal and chemical non-equilibrium, electro-magnetic interactions as well as particle collisions have to be considered. A common approach is to use particle-based methods. The Particle-in-Cell (PIC) method simulates charged collisionless gas flows by solving the Vlasov-Maxwel...

Recently, the Fokker–Planck (FP) kinetic model has been devised on the basis of the Boltzmann equation (Jenny et al., 2010; Gorji et al., 2011). Particle Monte-Carlo schemes are then introduced for simulations of rarefied gas flows based on the FP kinetics. Here the particles follow independent stochastic paths and thus a spatio-temporal resolution...

Laser ablation of metals has numerous applications, ranging from material processing to spacecraft propulsion. The impacting laser generates a plasma plume in front of a surface that expands into vacuum or a background medium. Different effects within the expanding plume are responsible for charge separation and particle acceleration1, which fundam...

In the field of material processing or spacecraft propulsion, laser ablation is used to remove material from a solid surface with a laser beam. The numerical study of this process has been directed towards direct laser-solid interactions, tackled by molecular dynamics simulations which have been conducted in the past. An additional field of interes...

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a...

Particle based methods are required to simulate rarefied, reactive plasma flows. A combined Particle-in-Cell Direct Simulation Monte Carlo method is used here, allowing the modelling of electromagnetic interactions and collision processes. The electromagnetic field solver of the Particle-in-Cell method has been improved by switching to a discontinu...

In a numerical solution of the Maxwell–Vlasov system, the consistency with the charge conservation and divergence conditions has to be kept solving the hyperbolic evolution equations of the Maxwell system, since the vector identity and/or the charge conservation of moving particles may be not satisfied completely due to discretization errors. One p...

Two new particle split and merge methods are presented for electromagnetic Particle-in-Cell codes. They are based on a statistical approach and are designed to conserve mass, momentum and energy. In addition, the correct spatial resolution of these values and the velocity distribution functions are reproduced. It is shown that charge and current de...

Plasma flows with high Knudsen numbers cannot be treated with classic continuum methods, as represented for example by the Navier–Stokes or the magnetohydrodynamic equations. Instead, the more fundamental Boltzmann equation has to be solved, which is done here approximately by particle based methods that also allow for thermal and chemical non-equi...

The ESA ACT Ariadna study 12/3201 is summarized. The study aims at resolving numerically the effects and phenomena leading to and occurring in a jet extraction inside a spherical Inertial Electrostatic Confinement device. The underlying numerical methodology and software is based on a Particle-In-Cell (PIC) code solving the full set of Maxwell equa...

A new particle pairing strategy is presented for the Direct Simulation Monte Carlo (DSMC) method. By combining Nearest Neighbour (NN) and Quad Tree Sort (QTS) algorithms, this modified DSMC method becomes largely independent of grid cell size. Therefore, the method possesses considerable advantages in terms of coupling with other grid-based methods...

Several advanced plasma propulsion designs have been developed and characterized at IRS in the past years. Among them are the hybrid thruster TIHTUS, the steady state applied-field thrusters AF-MPD ZT1 and ZT2 and advanced iMPD designs. These concepts show promising potential for future missions. The paper will discuss the designs and their operati...

We apply a particle code (Direct Simulation Monte Carlo, DSMC) to a nozzleflowexpansion set-up which is typical for thermal plasma spray systems. Although those systems tend to have a pressure level which is too high to be treated with DSMC we obtain good results with respect to Pitot pressure measurement based Mach number estimations at different...

More than three decades of experience have been gained in the field of electric propulsion at the Institute of Space Systems (Institut für Raumfahrtsysteme = IRS). Recent developments within the field of electric propulsion are summarized and foremost results are highlighted. The various types of electric propulsion systems are not considered as to...

The magnetic sail is a quite new concept of space propulsion utilising the solar wind in order to transfer momentum to a magnetic field source. The magnetic field size can be increased significantly by injecting a plasma into the center of the magnetic bubble. This concept is called Mini-Magnetospheric Plasma Propulsion (M2P2) system. The plasma in...

The magnetic sail is a quite new concept of space propulsion utilising the solar wind in order to transfer momentum to a magnetic field source. The magnetic field size can be increased significantly by injecting a plasma into the center of the magnetic bubble. This concept is called Mini-Magnetospheric Plasma Propulsion (M2P2) system. The plasma in...

Growing computational capabilities and simulation tools based on high-order methods allow for complex shaped plasma devices to simulate the entire nonlin-ear dynamics of the Vlasov-Maxwell system mod-elling the particle-field-interactions of a non-neutral plasma without significant simplifications [4]. Thereby, new insights into physics on a level...