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We investigate the flow in planar microscale nozzles and find that design and analysis paradigms based on the assumption of a dominant isentropic core with moderate viscosity corrections are not valid. Instead, the flow downstream of the throat is dominated by boundary layers that may choke the flow to subsonic velocities. The geometrical expansion ratio is found to be essentially irrelevant, instead, the length from throat to exit plane is found to be a much more important design parameter. Full 3D simulations are required to predict the flow topology; thermophysical modeling of the expanding gas has a noticeable impact on predicted performance. An analytical estimation of the Knudsen number in the expanding flow is given, allowing to determine its values from the expansion pressure ratio. An axial thrust analysis suggests truncation of the nozzle, resulting in a predicted 30% increase in thrust and 30% increase in specific impulse compared to the baseline configuration. The work has been carried out within the European Commission co-funded PRECISE project which was focused on designing and testing a micro chemical propulsion system thruster prototype using catalytically decomposed hydrazine as propellant.

The Jet Propulsion Laboratory (JPL) has pursued a multi-disciplinary effort to experimentally characterize and computationally simulate the effects of powered descent onto the Europan surface. As part of the proposed Europa Lander technology development and maturation activities, JPL Contamination Control and the German Aerospace Center (DLR) are conducting a test program to characterize monopropellant plume-induced contamination, the preliminary results of which are showcased in this presentation. These measurements have been used in the further development of JPL’s computational physics simulations of descent engine plumes interacting with the Europan surface with direct simulation Monte Carlo (DSMC) techniques, and in broader support of contamination control strategies for the proposed Europa Lander mission.

The flow through a thin slit and a thin orifice is studied with the Direct Simulation Monte Carlo (DSMC), cubic Fokker–Planck (FP), and a coupled FP-DSMC hybrid method. Pressure driven monatomic gas flows through a slit and an orifice with various values of degree of rarefaction and pressure ratio are computed. The DSMC method is physically accurate for all flow regimes; however it is computationally expensive in high density, near continuum regions. An alternative stochastic particle scheme, the cubic FP kinetic model has addressed this issue by approximating the particle collisions involved in the Boltzmann collision integral with continuous stochastic processes. The ability of the cubic FP method to reproduce breakdown of translational equilibrium is discussed. In addition, a coupled FP-DSMC hybrid scheme is employed aiming at an efficient and accurate solution. The FP-DSMC hybrid scheme employs DSMC in rarefied regions and FP method in near continuum flow regions. Numerical procedures of the cubic FP method are implemented within the framework of an existing DSMC-solver, SPARTA. The FP-DSMC hybrid solution reproduces pure DSMC solution with improved computational efficiency up to a factor of eight for vacuum flow through a thin slit.

In this work we investigate the kinetic Fokker-Planck (FP) model [1, 2] concerning its applicability to simulate hyper-sonic, rarefied gas flow. As in the direct simulation Monte Carlo (DSMC) algorithm, the FP model simulates the stochastic motion of a set of particles through the computational domain which results in a simple coupling of both methods. No collisions must be calculated in the FP approach and so larger cell and time step sizes than by DSMC calculations can be used. Because of this, the FP model holds the potential to be more efficient than DSMC where the Knudsen number is small. Further we present and investigate a hybridisation scheme for the FP and DSMC algorithms. We derive a non-equilibrium parameter from the Fokker-Planck- and Boltzmann-operator which indicates the validity of the FP model. In hybrid simulations this parameter is used to partition the computational domain in DSMC and FP regions. The particle motion is processed similarly in both regions, only the procedure for assigning new particle velocities differs. To achieve an equal number of particles per cell, weighting factors depended on the cell size are used. The hybridisation scheme is tested for one-dimensional shock and two-dimensional cylinder flows and gives results in agreement to pure DSMC simulations. An efficiency study shows, that the hybrid scheme is roughly five times faster than a pure DSMC simulation for a hypersonic cylinder flow test case.

The impact of two geometric configurations of sonic orifices on the free plume expansion into high vacuum is studied both experimentally and numerically. One configuration is a flat-faced cylinder, into whose face a square edged orifice is centrally machined. This simple type of orifice is often used for ease of manufacturing. The other source features a sharp-edged orifice, whose outer walls are inclined backwards 135o from the axis. Nitrogen plumes emanating at two source Reynolds numbers, Re* ∈ {3850, 15400}, are compared here. Mass flux measurements with a free-molecular impact pressure probe (“Patterson probe”) show, that the plume originating from the flat-faced orifice expands freely within about 45 o from the axis. Numerical analysis of the plume near-field suggests, that molecules scattered back from the walls of a conical orifice only affect the plume expansion at angles greater than about 80o from the axis.The impact of two geometric configurations of sonic orifices on the free plume expansion into high vacuum is studied both experimentally and numerically. One configuration is a flat-faced cylinder, into whose face a square edged orifice is centrally machined. This simple type of orifice is often used for ease of manufacturing. The other source features a sharp-edged orifice, whose outer walls are inclined backwards 135o from the axis. Nitrogen plumes emanating at two source Reynolds numbers, Re* ∈ {3850, 15400}, are compared here. Mass flux measurements with a free-molecular impact pressure probe (“Patterson probe”) show, that the plume originating from the flat-faced orifice expands freely within about 45 o from the axis. Numerical analysis of the plume near-field suggests, that molecules scattered back from the walls of a conical orifice only affect the plume expansion at angles greater than about 80o from the axis.

Kinetic Fokker–Planck (FP) methods for modeling rarefied gas flows have received increasing attention over the last few years. However, formulating such models for realistic multi-species gases is still an open subject of research. Therefore, in this letter, we develop a kinetic FP model for describing gas mixtures with particles interacting according to the variable hard-sphere interaction potential. In accordance with the kinetic FP framework, a stochastic solution algorithm is employed in order to solve the model on a particle level. Different test cases are carried out, and the performance of the proposed method is compared with the direct simulation Monte Carlo algorithm.

Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker-Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad's 13 moment equations on a Navier-Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He-Ar mixture.

The STG-CT, operated by the DLR Institute for Aerodynamics and Flow Technology in Göttingen, is a vacuum facility specically designed to provide and maintain a space-like vacuum environment for researching plume flow and plume impingement from satellite reaction control thrusters. Its unique liquid-helium driven cryopump of 30m2 allows maintaining a background pressure

Two identical, interacting plumes emanating from model thrusters with parallel axes separated from 50 to 150 throat diameters are studied numerically. The nozzle throat Reynolds number is set to nearly 15, 000 to match that of a small bi-propellant attitude control thruster, but the simulated gas is nitrogen with a stagnation temperature of 300 K. The near-isentropic, dense plume core is computed with the DLR Navier-Stokes solver TAU and the conditions at a suitably defined interface are then used on the inflow boundary of a separately conducted direct simulation Monte Carlo (DSMC) simulation. The results are shown to agree favorably with particle flux measurements performed in the DLR high-vacuum plume test facility for chemical thrusters (STG-CT). Varying the nozzle separation distance alters the degree of rarefaction in the interaction plane, and by tagging DSMC particles according to their origin, the effect on the individual plume may be investigated. The impact of nozzle axis separation on mass flux...

Background: Although increased conflicts between attitudes and beliefs about certain goals or values are often discussed as important factors in depression, there are only few empirical studies investigating these relations among patients with depressive disorders. Methods: In the present study, we used the Intrapersonal Conflict Test to assess cognitive inconsistencies in goals or values. A total of 53 inpatients with unipolar depression and 24 nondepressed controls (inpatients of an internal and a surgery ward) participated in the study. In addition to the Intrapersonal Conflict Test, patients completed the Beck Depression Inventory, the Dysfunctional Attitude Scale, the Inventory of Interpersonal Problems as well as the Problem Solving Inventory. Results: Compared with controls, patients with depressive disorders showed significantly higher scores for global inconsistencies, inconsistencies within different goals/values, as well as between goals/values and their perceived realization. Significant correlations were found between conflict measures and the Inventory of Interpersonal Problems, as well as the Problem Solving Inventory. Path analyses show that group differences in intrapersonal conflicts were partially mediated by interpersonal problems but not by depressive symptoms or cognitive vulnerability factors. Conclusions: Given the cross-sectional design of the study, the findings of this exploratory study do not allow for conclusions regarding the role of intrapersonal conflicts in the development and course of depression. Nevertheless, the high levels of intrapersonal conflicts observed in the study suggest that inconsistencies in goals or values should be considered in the psychological treatment of depression.

Flow in micro chemical propulsion systems (µCPS) based on etched silicon deviates strongly from its conventional, macroscopic counterparts. This paper reports on peculiarities of small scale planar nozzles with a high aspect ratio, rectangular cross section. Design and analysis paradigms based on the assumption of rationally symmetric flow with a dominant isentropic core are shown to be no longer valid. We will point out insufficiencies of treating planar nozzles as two dimensional, inviscid, or assessing their performance with classical analytical isentropic 1D analysis. Instead, the resulting low Reynolds number flow is boundary layer dominated. Boundary layer build-up from the top and bottom walls threaten to choke the expansion. The geometrical expansion ratio is found to be essentially irrelevant, the length from throat to exit plane is found to be a much more important design parameter. The work has been carried out within the European PRECISE project which is focused on designing and testing a prototype using catalytically decomposed hydrazine as propellant.

Clusters of orbital thrusters are an attractive option to achieve graduated thrust levels and increased redundancy with available hardware, but the heavily under-expanded plumes of chemical attitude control thrusters placed in close proximity will interact, leading to a local amplification of downstream fluxes and of back-flow onto the spacecraft. The interaction of two similar, parallel, axi-symmetric cold-gas model thrusters has recently been studied in the DLR High-Vacuum Plume Test Facility STG under space-like vacuum conditions, employing a Patterson-type impact pressure probe with slot orifice. We reproduce a selection of these experiments numerically, and emphasise that a comparison of numerical results to the measured data is not straight-forward. The signal of the probe used in the experiments must be interpreted according to the degree of rarefaction and local flow Mach number, and both vary dramatically thoughout the flow-field. We present a procedure to reconstruct the probe signal by post-processing the numerically obtained flow-field data and show that agreement to the experimental results is then improved. Features of the investigated cold-gas thruster plume interaction are discussed on the basis of the numerical results.

The free-molecular impact pressure probe, also known as Patterson probe, is known and applied for more than half a century now to deduce the number flux of a single species in highly rarefied inert flow. While the working principle is conceptually simple, interpretation of the gauge readings may not be, but approximate formulas for evaluation exist. In the context of cold-gas plume flow and interaction experiments with the obvious large variations in Mach and Knudsen numbers, it may not be clear initially, whether the signals measured with the Patterson probe are obtained in free-molecular flow environment, and hence, whether the mentioned evaluation techniques may be employed. A series of numerical experiments have been conducted using the Direct Simulation Monte-Carlo method, to study the response of the Patterson probe to prescribed free-stream conditions in the transitional flow regime. From the computational results we infer analytical expressions that describe the probe response in transitional regime at zero angle of attack.

The DSMC method simulates a gas by three uncoupled steps: moving representative particles through a physical domain, performing probabilistic collisions and estimating the macroscopic state by ensemble averaging. In order to ease computational treatment of these three steps it is convenient to discretize the space with a grid that fits into the boundaries of the physical domain. For efficient particle tracking it is useful that the cells of this grid are convex polyhedra which preferably have no indirect neighbors. To reduce discretization errors in the collision step and to take reasonable averages the cells should be nearly isotropic, whereas their volume is primarily determined by the local flow gradients. Especially the latter condition requires the density of the grid to be continuously adaptable in space and time. We show that grids derived from Voronoi diagrams fulfill these requirements very well.

This paper discusses features of a supersonic flow with a transversal Mach number stratification when encountering a ramp. A flow of this nature can occur for a variety of reasons around a hypersonic vehicle. Formation of a heated wall boundary layer, external fuel injection on the compression ramp, energy deposition, and film or transpiration cooling are just some of the processes that will establish a flow where a wall near layer features a distinct difference in Mach number compared to the outer flow. This paper will introduce a flow topology framework that will help to understand phenomena associated with this stratification. Shock refraction is identified as the main mechanism which causes a redirection of the flow additional to the ramp deflection. It will be shown how, depending on the Mach number ratios between the layers, shocks or expansion fans will be created that will interact with the surface. This can be the cause for undesired or unexpected temperature and pressure distributions along the wall when shock refraction is not taken into account. As a possible application, it will be shown how shock refraction can act as a virtual external compression ramp. CFD computations are performed using the DLR TAU code, a finite volume, second order accuracy, compressible flow solver.

Free-molecular pressure probes are employed to deduce particle flux in highly rarefied flow fields, such as the farfield or the backflow region of a plume expanding into vacuum. Analytical approaches to model the probe behavior are known in the literature for some time now. Numerical methods such as DSMC however allow to conduct investigations into the probe response in regimes inaccessible to analytical approaches. Besides, the numerical results may be compared to the analytical models in order to test their fidelity. We computed the response of a probe with slot orifice to a highly rarefied, parallel flow with varying molecular speed ratio. We confirmed the negligible influence of the speed ratio on probe response for low angles of attack, but observed significant deviations from analytical models as the angle of attack approaches 90°.

Laminar nitrogen flow expanding through a conical nozzle into high vacuum is to be numerically reproduced and compared to available experimental data. As the gas density varies quickly by several orders of magnitude, leading to high rarefaction and thermal non-equilibrium, standard (continuum) CFD tools are not sufficient to accurately model the expanding flow. In the work presented here, the efficiency of Navier-Stokes solvers is to be exploited where applicable, supplying the boundary conditions for a kinetic Direct Simulation Monte Carlo (DSMC) solver to handle the domain of rarefaction and non-equilibrium. The hypersonic character of the flow suggests to attempt a pure downstream coupling. The validity of this approach is to be verified.