Martin Grabe

Numerical Simulation of Nozzle Flow into High Vacuum Using Kinetic and Continuum Approaches

Laminar nitrogen flow expanding through a conical nozzle into high vacuum is 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 SimulationMonte 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.

Numerical Investigation of Two Interacting Parallel Thruster-Plumes and Comparison to Experiment

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-pro...

Flow Characteristics of Micro-Scale Planar Nozzles

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analysis paradigms based on the assumption of rationally symmetric flow with a dominant isentropic core are shown to be no longer valid.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.

Characterization of a Free-Molecular Pressure Probe employing Gas-Kinetic Simulation

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°.

Steady Shock Refraction in Hypersonic Ramp Flow

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.

Impact of nozzle separation on the plumes of two parallel thrusters

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...

A Voronoi Grid and a Particle Tracking Algorithm for DSMC

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.